From 491ecc2b9c6426386151e0b751dafd99bb3e8b23 Mon Sep 17 00:00:00 2001 From: Maria Marchwicka Date: Wed, 18 Nov 2020 20:05:10 +0100 Subject: [PATCH] is_function_big_for_all_metabolizers method --- cable_signature.sage | 80 +++++++++++++++++--------------------------- 1 file changed, 30 insertions(+), 50 deletions(-) diff --git a/cable_signature.sage b/cable_signature.sage index 422ef96..d08020b 100644 --- a/cable_signature.sage +++ b/cable_signature.sage @@ -9,6 +9,10 @@ from collections import Counter from sage.arith.functions import LCM_list import importlib + +SIGMA = 0 +SIGNATURE = 1 + def import_sage(module_name): importlib.invalidate_caches() @@ -40,7 +44,7 @@ class CableSummand(): self.signature_as_function_of_theta = \ self.get_summand_signature_as_theta_function() self.sigma_as_function_of_theta = \ - self.get_sigma_function() + self.get_sigma_as_function_of_theta() @staticmethod def get_summand_descrption(knot_as_k_values): @@ -194,33 +198,29 @@ class CableSummand(): for theta in range(range_limit): self.plot_summand_for_theta(theta) - def get_sigma_function(self): + def get_sigma_as_function_of_theta(self): last_k = self.knot_as_k_values[-1] last_q = 2 * abs(last_k) + 1 ksi = 1/last_q - def sigma_function(theta, print_results=False): + def sigma_as_function_of_theta(theta, print_results=False): # satellite part (Levine-Tristram signatures) - sp = 0 + satellite_part = 0 for i, k in enumerate(self.knot_as_k_values[:-1][::-1]): # print("layer") layer_num = i + 1 sigma_q = self.get_untwisted_signature_function(k) # print(sigma_q(ksi * theta * layer_num)) # print(sigma_q) - satelit_part = 2 * sigma_q(ksi * theta * layer_num) * sign(k) - sp += satelit_part + sp = 2 * sigma_q(ksi * theta * layer_num) * sign(k) + satellite_part += sp if theta: pp = (-last_q + 2 * theta - 2 * (theta^2/last_q)) * sign(last_k) else: pp = 0 - result = pp + sp - # print("pp = ", pp ) - # print("sp = ", sp) - # print(result) - return result - return sigma_function + return pp + satellite_part + return sigma_as_function_of_theta @@ -250,7 +250,6 @@ class CableSum(): self.get_sigma_as_function_of_theta() - def __call__(self, *thetas): return self.signature_as_function_of_theta(*thetas) @@ -333,7 +332,6 @@ class CableSum(): raise TypeError(msg) return tuple(thetas) - @staticmethod def get_knot_descrption(knot_sum): description = "" @@ -346,7 +344,15 @@ class CableSum(): description = description[:-2] + ") # " return description[:-3] - + def get_sigma_as_function_of_theta(self): + def sigma_as_function_of_theta(*thetas, **kwargs): + thetas = self.parse_thetas(*thetas) + result = 0 + for i, knot in enumerate(self.knot_summands): + sigma_of_th = knot.sigma_as_function_of_theta + result += sigma_of_th(thetas[i]) + return result + return sigma_as_function_of_theta def get_signature_as_function_of_theta(self, **key_args): if 'verbose' in key_args: @@ -425,7 +431,7 @@ class CableSum(): return False return True - def is_signature_big_for_all_metabolizers(self): + def is_function_big_for_all_metabolizers(self, function_type=SIGMA): num_of_summands = len(self.knot_sum_as_k_valus) if num_of_summands % 4: f_name = self.is_signature_big_for_all_metabolizers.__name__ @@ -438,25 +444,17 @@ class CableSum(): ranges_list[shift : shift + 3] = \ [range(0, i + 1) for i in self.patt_k_list[shift: shift + 3]] ranges_list[shift + 3] = range(0, 2) - if not self.is_signature_big_in_ranges(ranges_list): - return False + if function_type == SIGNATURE: + if not self.is_signature_big_in_ranges(ranges_list): + return False else: - print("\nOK") + if not self.is_sigma_big_in_ranges(ranges_list): + return False + print("\nOK") + return True - - def get_sigma_as_function_of_theta(self): - def sigma_as_function_of_theta(*thetas, **kwargs): - thetas = self.parse_thetas(*thetas) - result = 0 - for i, knot in enumerate(self.knot_summands): - sigma_of_th = knot.sigma_as_function_of_theta - result += sigma_of_th(thetas[i]) - return result - return sigma_as_function_of_theta - - def is_sigma_big_in_ranges(self, ranges_list): for thetas in it.product(*ranges_list): @@ -473,7 +471,7 @@ class CableSum(): # pp, sp, sf= self.signature_as_function_of_theta(*shifted_thetas) limit = 5 + np.count_nonzero(shifted_thetas) ext = self.sigma_as_function_of_theta(shifted_thetas) - print(ext) + # print(ext) extremum = abs(ext) if shift > 1: print(shifted_thetas, end=" ") @@ -490,24 +488,6 @@ class CableSum(): return False return True - def is_sigma_big_for_all_metabolizers(self): - num_of_summands = len(self.knot_sum_as_k_valus) - if num_of_summands % 4: - f_name = self.is_sima_big_for_all_metabolizers.__name__ - msg = "Function {}".format(f_name) + " is implemented only for " +\ - "knots that are direct sums of 4n direct summands." - raise ValueError(msg) - - for shift in range(0, num_of_summands, 4): - ranges_list = num_of_summands * [range(0, 1)] - ranges_list[shift : shift + 3] = \ - [range(0, i + 1) for i in self.patt_k_list[shift: shift + 3]] - ranges_list[shift + 3] = range(0, 2) - if not self.is_sigma_big_in_ranges(ranges_list): - return False - else: - print("\nOK") - return True