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