two cases and to loops for last theta
This commit is contained in:
Maria Marchwicka
parent
949344193c
commit
afbda34111
@ -7,7 +7,7 @@ import os
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import sys
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import collections
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import inspect
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# import inspect
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import itertools as it
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import numpy as np
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import re
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@ -32,34 +32,23 @@ class Config(object):
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self.verbose = True
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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_large_signature = True
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self.print_calculations_for_large_signature = False
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self.print_calculations_for_small_sigma = True
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self.print_calculations_for_small_sigma = False
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self.print_calculations_for_large_sigma = True
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self.print_calculations_for_large_sigma = 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.stop_after_firts_large_signature = True
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self.stop_after_firts_large_signature = False
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self.stop_after_firts_large_sigma = True
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self.stop_after_firts_large_sigma = False
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class SignatureFunction(object):
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"""
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This simple class encodes twisted and untwisted signature functions
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of knots. Since the signature function is entirely encoded by its signature
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jump, the class stores only information about signature jumps
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in a dictionary self.signature_jumps.
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The dictionary stores data of the signature jump as a key/values pair,
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where the key is the argument at which the functions jumps
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and value encodes the value of the jump. Remember that we treat
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signature functions as defined on the interval [0,1).
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"""
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def __init__(self, values=None, counter=None):
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# set values of signature jumps
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if counter is None:
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@ -74,29 +63,20 @@ class SignatureFunction(object):
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self.signature_jumps = collections.defaultdict(int, counter)
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def sum_of_absolute_values(self):
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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 sum([abs(i) for i in self.cnt_signature_jumps.values()])
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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.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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return not any(self.signature_jumps.values())
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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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for jump_arg, jump in self.cnt_signature_jumps.items():
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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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for jump_arg, jump in self.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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@ -138,12 +118,7 @@ class SignatureFunction(object):
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a = SignatureFunction(values=t_data)
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sf = SignatureFunction(values=new_data)
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sf2 = SignatureFunction(counter=counter)
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print(new_data)
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print(counter.items())
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assert a == sf
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print("repr")
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print(repr(sf2))
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print(repr(a))
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assert a == sf2
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return sf
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@ -165,10 +140,6 @@ class SignatureFunction(object):
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def __neg__(self):
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new_data = []
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print("neg")
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print("start values sign and cnt")
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print(self.signature_jumps.items())
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print(self.cnt_signature_jumps.items())
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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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a = SignatureFunction(values=new_data)
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@ -229,31 +200,19 @@ class SignatureFunction(object):
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arg = mod_one(arg)
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cnt = self.cnt_signature_jumps
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before_arg = [jump for jump_arg, jump in cnt.items() if jump_arg < arg]
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result = 2 * sum(before_arg) + cnt[arg]
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# TBD to delete
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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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assert result == val
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# end of to delete
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return result
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return 2 * sum(before_arg) + cnt[arg]
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def main(arg):
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try:
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new_limit = int(arg[1])
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except IndexError:
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new_limit = None
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search_for_large_signature_value(limit=new_limit)
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# search_for_null_signature_value(limit=new_limit)
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if arg[1]:
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limit = int(arg[1])
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else:
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limit = None
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search_for_large_signature_value(limit=limit)
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# search_for_null_signature_value(limit=limit)
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# searching for signture > 5 + #(v_i != 0) over given knot schema
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# searching for sigma > 5 + #(v_i != 0) over given knot schema
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def search_for_large_signature_value(knot_formula=None,
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limit=None,
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verbose=None):
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@ -272,6 +231,8 @@ def search_for_large_signature_value(knot_formula=None,
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P = Primes()
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good_knots = []
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# with open(config.f_results, 'w') as f_results:
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# iterate over q-vector
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for c in combinations:
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k = [(P.unrank(i) - 1)/2 for i in c]
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if config.only_slice_candidates:
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@ -281,20 +242,20 @@ def search_for_large_signature_value(knot_formula=None,
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if verbose:
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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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print_results=False)
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result = eval_cable_for_large_sigma(k_vector=k,
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knot_formula=knot_formula,
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print_results=False)
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good_knots.append(result)
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return good_knots
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# searching for signture > 5 + #(v_i != 0)
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def eval_cable_for_large_signature(k_vector=None,
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knot_formula=None,
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print_results=True,
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verbose=None,
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q_vector=None):
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# searching for sigma > 5 + #(v_i != 0)
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def eval_cable_for_large_sigma(k_vector=None,
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knot_formula=None,
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print_results=True,
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verbose=None,
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q_vector=None):
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if knot_formula is None:
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knot_formula = config.knot_formula
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if verbose is None:
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@ -306,11 +267,22 @@ def eval_cable_for_large_signature(k_vector=None,
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return None
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else:
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k_vector = [(i - 1)/2 for i in q_vector]
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k = k_vector
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knot_sum = eval(knot_formula)
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if len(knot_sum) != 4:
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print("Wrong number of cable direct summands!")
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return None
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knot_description = get_knot_descrption(*knot_sum)
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return _eval_cable_for_large_sigma(k_vector, knot_description,
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print_results, verbose)
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def _eval_cable_for_large_sigma(k, knot_description, print_results, verbose):
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# k is a k_vector
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print("\n" * 5)
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print(knot_description)
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k_1, k_2, k_3, k_4 = [abs(i) for i in k]
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q_4 = 2 * k_4 + 1
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ksi = 1/q_4
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@ -321,120 +293,221 @@ def eval_cable_for_large_signature(k_vector=None,
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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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return None
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large_sigma_for_all_v_comninations = True
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good_knots = [("nic")]
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large_sigma_for_all_v_combinations = True
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bad_vectors = []
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good_vectors = []
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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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theta_squers = [i^2 for i in v_theta]
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condition = "(" + str(theta_squers[0]) \
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+ " - " + str(theta_squers[1]) \
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+ " + " + str(theta_squers[2]) \
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+ " - " + str(theta_squers[3]) \
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+ ") % " + str(q_4)
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# if verbose:
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# print "\nChecking for characters: " + str(v_theta)
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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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# 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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sigma_q_1 = get_untwisted_signature_function(k_1)
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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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# large_sigma_for_last_theta_non_zero = True
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#!!!!!!!!!!!!!!!!
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# consider a_4 non-zero and zero
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last_theta = 1
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large_sigma_for_last_theta_non_zero = True
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for vector in it.product(3 * [range(q_4)]):
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v_theta = list(vector)
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v_theta.append(last_theta)
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a_1, a_2, a_3 = vector
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a_4 = last_theta
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assert [a_1, a_2, a_3, a_4] == v_theta
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if a_1 == a_2 == a_3:
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if a_3 == 0:
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print("\na_1 == a_2 == a_3 == 0")
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continue
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elif a_3 == a_4:
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print("\nall a_i == a != 0")
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continue
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if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
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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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# print("\t\t\tMultiplication of the vector " + str(v_theta))
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large_sigma_for_this_vector = False
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for shift in range(1, q_4):
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# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
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shifted_theta = [(shift * a) % q_4 for a in
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[a_1, a_2, a_3, a_4]]
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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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# "untwisted" part (Levine-Tristram signatures)
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a_1, a_2, a_3, a_4 = shifted_theta
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untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
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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_1 * 2) -
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sigma_q_1(ksi * a_4 * 2))
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# "untwisted" part (Levine-Tristram signatures)
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sigma_q_1 = get_untwisted_signature_function(k_1)
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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(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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for i, a in enumerate(shifted_theta):
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if a:
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tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
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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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# "twisted" part
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tp = [0, 0, 0, 0]
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for i, a in enumerate(v_theta):
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if a:
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tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
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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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sigma_v = untwisted_part + twisted_part
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# print(knot_description + "\t" + str(shifted_theta) +\
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# "\t" + str(sigma_v))
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# + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
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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: ", 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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else:
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print(knot_description + "\t" + str(v_theta) +\
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"\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
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if config.stop_after_firts_large_signature:
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break
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if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
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large_sigma_for_this_vector = True
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if large_sigma_for_this_vector:
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good_vectors.append(shifted_theta)
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pass
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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_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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else:
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print(knot_description + "\t" + str(v_theta) +\
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"\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
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bad_vectors.append(shifted_theta)
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large_sigma_for_last_theta_non_zero = False
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last_theta = 0
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large_sigma_for_last_theta_zero = True
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for vector in it.product(3 * [range(q_4)]):
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v_theta = list(vector)
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v_theta.append(last_theta)
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a_1, a_2, a_3 = vector
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a_4 = last_theta
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assert [a_1, a_2, a_3, a_4] == v_theta
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if a_1 == a_2 == a_3:
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if a_3 == 0:
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print("\na_1 == a_2 == a_3 == 0")
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continue
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elif a_3 == a_4:
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print("\nall a_i == a != 0")
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continue
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if (a_1^2 - a_2^2 + a_3^2 - a_4^2) % q_4:
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continue
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# print("\t\t\tMultiplication of the vector " + str(v_theta))
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large_sigma_for_this_vector = False
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for shift in range(1, q_4):
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# print("shift = " + str(shift) + ", q_4 = " + str(q_4))
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shifted_theta = [(shift * a) % q_4 for a in
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[a_1, a_2, a_3, a_4]]
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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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# "untwisted" part (Levine-Tristram signatures)
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a_1, a_2, a_3, a_4 = shifted_theta
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untwisted_part = 2 * (sigma_q_2(ksi * a_1) -
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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_1 * 2) -
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sigma_q_1(ksi * a_4 * 2))
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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))
|
||||
# "twisted" part
|
||||
tp = [0, 0, 0, 0]
|
||||
for i, a in enumerate(shifted_theta):
|
||||
if a:
|
||||
tp[i] = -q_4 + 2 * a - 2 * (a^2/q_4)
|
||||
twisted_part = tp[0] - tp[1] + tp[2] - tp[3]
|
||||
# assert twisted_part == int(twisted_part)
|
||||
|
||||
# else:
|
||||
# print "\n\tSmall signature value"
|
||||
# print knot_description
|
||||
# print "v_theta: " + str(v_theta)
|
||||
# print condition
|
||||
# print "non zero value in v_theta: " + str(np.count_nonzero(v_theta))
|
||||
# print "signature at 1/2: " + str(y)
|
||||
return good_knots
|
||||
sigma_v = untwisted_part + twisted_part
|
||||
# print(knot_description + "\t" + str(shifted_theta) +\
|
||||
# "\t" + str(sigma_v))
|
||||
# + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
||||
|
||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
||||
large_sigma_for_this_vector = True
|
||||
# break
|
||||
# else:
|
||||
# pass
|
||||
# print(knot_description + "\t" + \
|
||||
# str(shifted_theta) +\
|
||||
# "\t" + str(sigma_v))
|
||||
|
||||
|
||||
if large_sigma_for_this_vector:
|
||||
good_vectors.append(shifted_theta)
|
||||
pass
|
||||
# print("large_sigma_for_this_vector\n\n\n\n")
|
||||
# print("\n\nHURA HURA")
|
||||
else:
|
||||
# print(shifted_theta)
|
||||
# if a_3 == a_4:
|
||||
# print(sigma_q_1(ksi * a_4 * 2))
|
||||
bad_vectors.append(shifted_theta)
|
||||
large_sigma_for_last_theta_zero = False
|
||||
# break
|
||||
|
||||
if large_sigma_for_last_theta_non_zero and large_sigma_for_last_theta_zero:
|
||||
print(100 * "\n\nHURA HURA")
|
||||
print(knot_description)
|
||||
|
||||
# # if config.print_calculations_for_large_sigma:
|
||||
# # print("*" * 100)
|
||||
# # print("\n\nLarge signature value\n")
|
||||
# # print(knot_description)
|
||||
# # print("\nv_theta: ", end="")
|
||||
# # print(v_theta)
|
||||
# # print("k values: ", end="")
|
||||
# # print(str(k_1) + " " + str(k_2) + " " + \
|
||||
# # str(k_3) + " " + str(k_4))
|
||||
# # print(condition)
|
||||
# # print("non zero value in v_theta: " + \
|
||||
# # str(np.count_nonzero(v_theta)))
|
||||
# # print("sigma_v: " + str(sigma_v))
|
||||
# # print("\ntwisted_part: ", end="")
|
||||
# # print(twisted_part)
|
||||
# # print("untwisted_part: ", end="")
|
||||
# # print(untwisted_part)
|
||||
# # print("\n\nCALCULATIONS")
|
||||
# # print("*" * 100)
|
||||
# # sults_LT(v_theta, knot_description,
|
||||
# # ksi, untwisted_part,
|
||||
# # k, sigma_q_1, sigma_q_2, sigma_q_3)
|
||||
# # sults_sigma(v_theta, knot_description, tp, q_4)
|
||||
# # print("*" * 100 + "\n" * 5)
|
||||
# # else:
|
||||
# # print(knot_description + "\t" + str(v_theta) +\
|
||||
# # "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
||||
# # # if config.stop_after_firts_large_sigma:
|
||||
# # # break
|
||||
# # # sigma is small
|
||||
# # else:
|
||||
# # if config.print_calculations_for_small_sigma:
|
||||
# # print("\n" * 5 + "*" * 100)
|
||||
# # print("\nSmall signature value\n")
|
||||
# # print(knot_description)
|
||||
# # print_results_LT(v_theta, knot_description, ksi, untwisted_part,
|
||||
# # k, sigma_q_1, sigma_q_2, sigma_q_3)
|
||||
# # print_results_sigma(v_theta, knot_description, tp, q_4)
|
||||
# # print("*" * 100 + "\n" * 5)
|
||||
# # large_sigma_for_all_v_combinations = False
|
||||
# #
|
||||
# # if not config.print_calculations_for_small_sigma:
|
||||
# # print(knot_description + "\t" + str(v_theta) +\
|
||||
# # "\t" + str(sigma_v) + "\t" + str(2 * sigma_q_1(2 * ksi * a_4)))
|
||||
# #
|
||||
# #
|
||||
# # # print("ojojojoj")
|
||||
# # # break
|
||||
#
|
||||
# if large_sigma_for_all_v_combinations:
|
||||
# print("\n\n\nHura hura")
|
||||
# good_knots.append((knot_description, v_theta))
|
||||
#
|
||||
# # else:
|
||||
# # print "\n\tSmall signature value"
|
||||
# # print knot_description
|
||||
# # print "v_theta: " + str(v_theta)
|
||||
# # print condition
|
||||
# # print "non zero value in v_theta: " + str(np.count_nonzero(v_theta))
|
||||
# # print "signature at 1/2: " + str(y)
|
||||
print("\ngood_vectors")
|
||||
print(good_vectors)
|
||||
print("\nbad_vectors")
|
||||
print(bad_vectors)
|
||||
return None
|
||||
|
||||
|
||||
def print_results_LT(v_theta, knot_description, ksi, untwisted_part,
|
||||
@ -947,7 +1020,17 @@ get_signature_summand_as_theta_function.__doc__ = \
|
||||
a function that returns SignatureFunction for this single cable
|
||||
and a theta given as an argument
|
||||
"""
|
||||
|
||||
SignatureFunction.__doc__ = \
|
||||
"""
|
||||
This simple class encodes twisted and untwisted signature functions
|
||||
of knots. Since the signature function is entirely encoded by its signature
|
||||
jump, the class stores only information about signature jumps
|
||||
in a dictionary self.signature_jumps.
|
||||
The dictionary stores data of the signature jump as a key/values pair,
|
||||
where the key is the argument at which the functions jumps
|
||||
and value encodes the value of the jump. Remember that we treat
|
||||
signature functions as defined on the interval [0,1).
|
||||
"""
|
||||
get_signture_function_docsting = \
|
||||
"""
|
||||
This function returns SignatureFunction for previously defined single
|
||||
|
||||
Loading…
Reference in New Issue
Block a user