add property in CableTorus
This commit is contained in:
Maria Marchwicka
parent
acbf651697
commit
c51064abf0
@ -14,21 +14,20 @@ SIGMA = 1
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class SignatureFunction(object):
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class SignatureFunction(object):
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def __init__(self, values=None, counter=None):
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def __init__(self, values=None, counter=None):
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# set values of signature jumps
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# builed counter based on values of signature jumps
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if counter is None:
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if counter is None:
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counter = collections.Counter()
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counter = collections.Counter()
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if values is None:
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if values is None:
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values = []
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values = []
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else:
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msg = "Signature function is defined on the interval [0, 1)."
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msg = "Signature function is defined on the interval [0, 1)."
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assert all(k < 1 for k, v in values), msg
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assert all(k < 1 for k, v in values), msg
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counter2 = collections.Counter({ k : v for k, v in values})
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for k, v in values:
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for k, v in values:
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counter[k] += v
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counter[k] += v
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assert counter2 == counter
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self.cnt_signature_jumps = counter
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self.cnt_signature_jumps = counter
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self.tikz_plot("bum.tex")
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# self.tikz_plot("bum.tex")
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def is_zero_everywhere(self):
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def is_zero_everywhere(self):
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@ -41,7 +40,6 @@ class SignatureFunction(object):
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counter.update(collections.Counter({ k / 2 : v for k, v in items}))
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counter.update(collections.Counter({ k / 2 : v for k, v in items}))
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new_data = []
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new_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.cnt_signature_jumps.items():
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if jump != 0:
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new_data.append((jump_arg/2, jump))
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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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new_data.append((1/2 + jump_arg/2, jump))
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assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
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assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
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@ -60,7 +58,6 @@ class SignatureFunction(object):
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counter[2 * jump_arg] = jump
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counter[2 * jump_arg] = jump
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assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
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assert SignatureFunction(values=new_data) == SignatureFunction(counter=counter)
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return SignatureFunction(values=new_data)
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return SignatureFunction(values=new_data)
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def minus_square_root(self):
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def minus_square_root(self):
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@ -202,47 +199,100 @@ class SignatureFunction(object):
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class TorusCable(object):
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class TorusCable(object):
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def __init__(self, knot_formula, k_vector=None, q_vector=None):
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def __init__(self, knot_formula, k_vector=None, q_vector=None):
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self._knot_formula = knot_formula
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# q_i = 2 * k_i + 1
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# q_i = 2 * k_i + 1
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if k_vector is None:
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if k_vector is not 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) \
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or q values (q_vector).")
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msg = ""
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raise ValueError(msg)
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else:
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k_vector = [(q - 1)/2 for q in q_vector]
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elif q_vector is None:
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q_vector = [2 * k + 1 for k in k_vector]
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self.knot_formula = knot_formula
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self.k_vector = k_vector
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self.k_vector = k_vector
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elif q_vector is not None:
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self.q_vector = q_vector
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self.q_vector = q_vector
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k = k_vector
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else:
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self.knot_sum = eval(knot_formula)
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msg = "Please give a list of k (k_vector) or q values (q_vector)."
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self.knot_description = self.set_knot_descrption()
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raise ValueError(msg)
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self.__sigma_function = None
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# TBD property function
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# TBD property function
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self.signature_as_function_of_theta = None
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self._sigma_function = None
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self.signature_as_function_of_theta = self.get_signature_as_function_of_theta()
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self._signature_as_function_of_theta = None
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# self.signature_as_function_of_theta = None
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# SIGMA & SIGNATURE
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@property
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def sigma_function(self):
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if self._sigma_function is None:
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self._sigma_function = self.get_sigma_function()
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return self._sigma_function
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@property
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def signature_as_function_of_theta(self):
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if self._signature_as_function_of_theta is None:
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self._signature_as_function_of_theta = \
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self.get_signature_as_function_of_theta()
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return self._signature_as_function_of_theta
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@property
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def knot_formula(self):
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return self._knot_formula
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@property
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def knot_description(self):
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return self._knot_description
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@property
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def knot_sum(self):
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return self._knot_sum
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@knot_sum.setter
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def knot_sum(self, val):
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self._knot_sum = val
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self._knot_description = self.get_knot_descrption(val)
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self._number_of_summands = len(val)
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@property
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def number_of_summands(self):
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return self._number_of_summands
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@property
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def k_vector(self):
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return self._k_vector
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@k_vector.setter
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def k_vector(self, k):
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self._k_vector = k
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self.knot_sum = eval(self.knot_formula)
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self._q_vector = [2 * k_val + 1 for k_val in k]
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@property
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def q_vector(self):
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return self._q_vector
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@q_vector.setter
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def q_vector(self, new_q_vector):
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self.k_vector = [(q - 1)/2 for q in new_q_vector]
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def update(self, other):
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def update(self, other):
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# TBD knot_formula etc.
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# TBD knot_formula etc.
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number_of_summands = len(self.knot_sum)
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print("*" * 100)
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self.knot_description += " # " + other.knot_description
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print("BEFORE")
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self.knot_formula = self.knot_formula[:-1] + ",\n" + \
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other.knot_formula[1:]
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print(self.knot_sum)
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self.knot_sum += other.knot_sum
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# self.signature_as_function_of_theta = \
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# self.get_signature_as_function_of_theta() + \
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# other.get_signature_as_function_of_theta()
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print(self.knot_description)
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print(self.knot_description)
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print(self.knot_formula)
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print(self.knot_formula)
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print(self.knot_sum)
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print(self.knot_sum)
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def __get_sigma_function(self):
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self._knot_formula = self.knot_formula[:-1] + ",\n" + \
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other.knot_formula[1:]
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self.knot_sum += other.knot_sum
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# self.signature_as_function_of_theta = \
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# self.get_signature_as_function_of_theta() + \
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# other.get_signature_as_function_of_theta()
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print("*" * 100)
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print("AFTER")
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print(self.knot_description)
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print(self.knot_formula)
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print(self.knot_sum)
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def get_sigma_function(self):
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k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
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k_1, k_2, k_3, k_4 = [abs(k) for k in self.k_vector]
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last_q = 2 * k_4 + 1
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last_q = 2 * k_4 + 1
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ksi = 1/last_q
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ksi = 1/last_q
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@ -273,71 +323,6 @@ class TorusCable(object):
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return sigma_v
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return sigma_v
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return sigma_function
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return sigma_function
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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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verbose_default = key_args['verbose']
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else:
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verbose_default = False
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def signature_as_function_of_theta(*thetas, **kwargs):
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verbose = verbose_default
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if 'verbose' in kwargs:
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verbose = kwargs['verbose']
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len_a = len(self.knot_sum)
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len_t = len(thetas)
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# call with no arguments
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if len_t == 0:
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return signature_as_function_of_theta(*(len_a * [0]))
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if len_t != len_a:
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if isinstance(thetas, Iterable) and len(thetas[0]) == len_a:
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thetas = thetas[0]
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else:
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msg = "This function takes exactly " + str(len_a) + \
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" arguments or no argument at all (" + str(len_t) + \
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" given)."
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raise TypeError(msg)
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sf = SignatureFunction()
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untwisted_part = SignatureFunction()
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# for each cable knot in cable sum apply theta
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for i, knot in enumerate(self.knot_sum):
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try:
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ssf = self.get_summand_signature_as_theta_function(*knot)
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plus, _, up = ssf(thetas[i])
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# sf += ssf(thetas[i])
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sf += plus
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untwisted_part += up
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# in case wrong theata value was given
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except ValueError as e:
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print("ValueError: " + str(e.args[0]) +\
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" Please change " + str(i + 1) + ". parameter.")
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return None
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a = thetas[0]
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if all(i == a or i == self.q_vector[-1] - a for i in thetas):
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print()
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print("\n" + "*" * 100)
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print(self.knot_description)
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print("one vector " + str(thetas))
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print("max sf " + str(sf.is_big()))
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print()
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# assert untwisted_part.is_zero_everywhere()
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if verbose:
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print()
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print(str(thetas))
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print(sf)
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msg = "tota signature jump = " + str(sf.total_sign_jump())
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msg += "\nfunction\n" + str(sf)
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assert sf.total_sign_jump() == 0, msg
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return sf
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signature_as_function_of_theta.__doc__ =\
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signature_as_function_of_theta_docstring
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return signature_as_function_of_theta
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@staticmethod
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@staticmethod
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def get_blanchfield_for_pattern(k_n, theta):
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def get_blanchfield_for_pattern(k_n, theta):
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if theta == 0:
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if theta == 0:
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@ -395,7 +380,6 @@ class TorusCable(object):
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return SignatureFunction(values=results)
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return SignatureFunction(values=results)
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@staticmethod
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@staticmethod
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def get_untwisted_signature_function(j):
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def get_untwisted_signature_function(j):
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# return the signature function of the T_{2,2k+1} torus knot
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# return the signature function of the T_{2,2k+1} torus knot
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@ -406,10 +390,10 @@ class TorusCable(object):
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for a in range(k + 1, 2 * k + 1)])
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for a in range(k + 1, 2 * k + 1)])
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return SignatureFunction(values=w)
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return SignatureFunction(values=w)
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@staticmethod
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def set_knot_descrption(self):
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def get_knot_descrption(knot_sum):
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description = ""
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description = ""
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for knot in self.knot_sum:
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for knot in knot_sum:
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if knot[0] < 0:
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if knot[0] < 0:
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description += "-"
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description += "-"
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description += "T("
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description += "T("
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@ -418,11 +402,69 @@ class TorusCable(object):
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description = description[:-2] + ") # "
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description = description[:-2] + ") # "
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return description[:-3]
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return description[:-3]
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def get_signature_as_function_of_theta(self, verbose=False):
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if self.signature_as_function_of_theta is None:
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def get_signature_as_function_of_theta(self, **key_args):
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self.signature_as_function_of_theta = \
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if 'verbose' in key_args:
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self.__get_signature_as_function_of_theta(verbose=verbose)
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verbose_default = key_args['verbose']
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return self.signature_as_function_of_theta
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else:
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verbose_default = False
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def signature_as_function_of_theta(*thetas, **kwargs):
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verbose = verbose_default
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if 'verbose' in kwargs:
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verbose = kwargs['verbose']
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len_a = len(self.knot_sum)
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len_t = len(thetas)
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# call with no arguments
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if len_t == 0:
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return signature_as_function_of_theta(*(len_a * [0]))
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if len_t != len_a:
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if isinstance(thetas, Iterable) and len(thetas[0]) == len_a:
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thetas = thetas[0]
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else:
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msg = "This function takes exactly " + str(len_a) + \
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" arguments or no argument at all (" + str(len_t) + \
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" given)."
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raise TypeError(msg)
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sf = SignatureFunction()
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untwisted_part = SignatureFunction()
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# for each cable knot in cable sum apply theta
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for i, knot in enumerate(self.knot_sum):
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try:
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ssf = self.get_summand_signature_as_theta_function(*knot)
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plus, _, up = ssf(thetas[i])
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# sf += ssf(thetas[i])
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sf += plus
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untwisted_part += up
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# in case wrong theata value was given
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except ValueError as e:
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print("ValueError: " + str(e.args[0]) +\
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" Please change " + str(i + 1) + ". parameter.")
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return None
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a = thetas[0]
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if all(i == a or i == self.q_vector[-1] - a for i in thetas):
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print()
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print("\n" + "*" * 100)
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print(self.knot_description)
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print("one vector " + str(thetas))
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print("max sf " + str(sf.is_big()))
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print()
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# assert untwisted_part.is_zero_everywhere()
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if verbose:
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print()
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print(str(thetas))
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print(sf)
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msg = "tota signature jump = " + str(sf.total_sign_jump())
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msg += "\nfunction\n" + str(sf)
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assert sf.total_sign_jump() == 0, msg
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return sf
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signature_as_function_of_theta.__doc__ =\
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signature_as_function_of_theta_docstring
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return signature_as_function_of_theta
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def get_summand_signature_as_theta_function(self, *knot_as_k_values):
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def get_summand_signature_as_theta_function(self, *knot_as_k_values):
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def get_summand_signture_function(theta):
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def get_summand_signture_function(theta):
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@ -464,46 +506,28 @@ class TorusCable(object):
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number_of_combinations *= (2 * abs(knot[-1]) + 1)
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number_of_combinations *= (2 * abs(knot[-1]) + 1)
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return number_of_combinations
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return number_of_combinations
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# to be removed
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def check_combinations_in_range(self, range_product):
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if self.__sigma_function is None:
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self.__sigma_function = self.__get_sigma_function()
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return self.__check_combinations_in_range(range_product, SIGMA)
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# to be removed
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def calculate_sigma(self, theta_vector):
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if self.__sigma_function is None:
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self.__sigma_function = self.__get_sigma_function()
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return self.__sigma_function(theta_vector)
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def is_sigma_for_vector_class_big(self, theta_vector):
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if self.__sigma_function is None:
|
|
||||||
self.__sigma_function = self.__get_sigma_function()
|
|
||||||
return self.__is_value_for_vector_class_big(theta_vector, SIGMA)
|
|
||||||
|
|
||||||
|
|
||||||
# searching for signature == 0
|
# searching for signature == 0
|
||||||
def check_for_null_theta_combinations(self, verbose=False):
|
def check_for_null_theta_combinations(self, verbose=False):
|
||||||
list_of_good_vectors= []
|
list_of_good_vectors= []
|
||||||
number_of_null_comb = 0
|
number_of_null_comb = 0
|
||||||
f = self.get_signature_as_function_of_theta(verbose=verbose)
|
f = self.signature_as_function_of_theta
|
||||||
range_list = [range(abs(knot[-1]) + 1) for knot in self.knot_sum]
|
range_list = [range(abs(knot[-1]) + 1) for knot in self.knot_sum]
|
||||||
for theta_vector in it.product(*range_list):
|
for theta_vector in it.product(*range_list):
|
||||||
if f(*theta_vector, verbose=False).is_zero_everywhere():
|
if f(*theta_vector).is_zero_everywhere():
|
||||||
list_of_good_vectors.append(theta_vector)
|
list_of_good_vectors.append(theta_vector)
|
||||||
m = len([theta for theta in theta_vector if theta != 0])
|
m = len([theta for theta in theta_vector if theta != 0])
|
||||||
number_of_null_comb += 2^m
|
number_of_null_comb += 2^m
|
||||||
return number_of_null_comb, list_of_good_vectors
|
return number_of_null_comb, list_of_good_vectors
|
||||||
|
|
||||||
# searching for sigma > 5 + #(v_i != 0)
|
# searching for signature or sigma > 5 + #(v_i != 0)
|
||||||
def __check_all_combinations_in_ranges(self, list_of_ranges,
|
def check_all_combinations_in_ranges(self, list_of_ranges,
|
||||||
sigma_or_sign,
|
sigma_or_sign,
|
||||||
print_results=False):
|
print_results=False):
|
||||||
all_combinations_pass = True
|
all_combinations_pass = True
|
||||||
all_bad_vectors = []
|
all_bad_vectors = []
|
||||||
number_of_all_good_v = 0
|
number_of_all_good_v = 0
|
||||||
for i, range_product in enumerate(list_of_ranges):
|
for i, range_product in enumerate(list_of_ranges):
|
||||||
good_v, bad_v = self.__check_combinations_in_range(range_product,
|
good_v, bad_v = self.check_combinations_in_range(range_product,
|
||||||
sigma_or_sign)
|
sigma_or_sign)
|
||||||
number_of_all_good_v += len(good_v)
|
number_of_all_good_v += len(good_v)
|
||||||
all_bad_vectors = list(it.chain(all_bad_vectors, bad_v))
|
all_bad_vectors = list(it.chain(all_bad_vectors, bad_v))
|
||||||
@ -523,7 +547,7 @@ class TorusCable(object):
|
|||||||
return all_combinations_pass
|
return all_combinations_pass
|
||||||
|
|
||||||
# searching for signature or sigma > 5 + #(v_i != 0)
|
# searching for signature or sigma > 5 + #(v_i != 0)
|
||||||
def __check_combinations_in_range(self, range_product, sigma_or_sign):
|
def check_combinations_in_range(self, range_product, sigma_or_sign):
|
||||||
bad_vectors = []
|
bad_vectors = []
|
||||||
good_vectors = []
|
good_vectors = []
|
||||||
last_q = self.q_vector[-1]
|
last_q = self.q_vector[-1]
|
||||||
@ -536,7 +560,7 @@ class TorusCable(object):
|
|||||||
# pass
|
# pass
|
||||||
# else:
|
# else:
|
||||||
# continue
|
# continue
|
||||||
if self.__is_value_for_vector_class_big(vector, sigma_or_sign):
|
if self.is_value_for_vector_class_big(vector, sigma_or_sign):
|
||||||
good_vectors.append(vector)
|
good_vectors.append(vector)
|
||||||
else:
|
else:
|
||||||
# print(vector)
|
# print(vector)
|
||||||
@ -565,7 +589,7 @@ class TorusCable(object):
|
|||||||
|
|
||||||
# check sigma or signature function value
|
# check sigma or signature function value
|
||||||
# for all v = s * [a_1, a_2, a_3, a_4] for s in [1, last_q - 1]
|
# for all v = s * [a_1, a_2, a_3, a_4] for s in [1, last_q - 1]
|
||||||
def __is_value_for_vector_class_big(self, theta_vector, sigma_or_sign):
|
def is_value_for_vector_class_big(self, theta_vector, sigma_or_sign):
|
||||||
[a_1, a_2, a_3, a_4] = theta_vector
|
[a_1, a_2, a_3, a_4] = theta_vector
|
||||||
q_4 = self.q_vector[-1]
|
q_4 = self.q_vector[-1]
|
||||||
k_4 = self.k_vector[-1]
|
k_4 = self.k_vector[-1]
|
||||||
@ -575,7 +599,7 @@ class TorusCable(object):
|
|||||||
if sigma_or_sign == SIGNATURE:
|
if sigma_or_sign == SIGNATURE:
|
||||||
f = self.signature_as_function_of_theta
|
f = self.signature_as_function_of_theta
|
||||||
else:
|
else:
|
||||||
f = self.__sigma_function
|
f = self.sigma_function
|
||||||
# print(theta_vector, end="\t")
|
# print(theta_vector, end="\t")
|
||||||
|
|
||||||
for shift in range(1, k_4 + 1):
|
for shift in range(1, k_4 + 1):
|
||||||
@ -583,13 +607,13 @@ class TorusCable(object):
|
|||||||
[a_1, a_2, a_3, a_4]]
|
[a_1, a_2, a_3, a_4]]
|
||||||
if sigma_or_sign == SIGNATURE:
|
if sigma_or_sign == SIGNATURE:
|
||||||
sf = f(shifted_theta)
|
sf = f(shifted_theta)
|
||||||
sigma_v = sf.is_big()
|
sig_v = sf.is_big()
|
||||||
else:
|
else:
|
||||||
sigma_v = f(shifted_theta)
|
sig_v = f(shifted_theta)
|
||||||
print(sigma_v, end=" ")
|
print(sig_v, end=" ")
|
||||||
if abs(sigma_v) > abs(max_sigma):
|
if abs(sig_v) > abs(max_sigma):
|
||||||
max_sigma = sigma_v
|
max_sig = sig_v
|
||||||
if abs(sigma_v) > 5 + np.count_nonzero(shifted_theta):
|
if abs(sig_v) > 5 + np.count_nonzero(shifted_theta):
|
||||||
# print("\tok " + str(sigma_v))
|
# print("\tok " + str(sigma_v))
|
||||||
return True
|
return True
|
||||||
# print("\tbad class " + str(max_sigma))
|
# print("\tbad class " + str(max_sigma))
|
||||||
@ -602,15 +626,7 @@ class TorusCable(object):
|
|||||||
verbose=False):
|
verbose=False):
|
||||||
if print_results:
|
if print_results:
|
||||||
print(self.knot_description) # , end="\t\t\t")
|
print(self.knot_description) # , end="\t\t\t")
|
||||||
if sigma_or_sign == SIGMA:
|
if self.check_all_combinations_in_ranges(list_of_ranges,
|
||||||
if self.__sigma_function is None:
|
|
||||||
self.__sigma_function = self.__get_sigma_function()
|
|
||||||
else:
|
|
||||||
if self.signature_as_function_of_theta is None:
|
|
||||||
self.signature_as_function_of_theta= \
|
|
||||||
self.__get_signature_as_function_of_theta()
|
|
||||||
|
|
||||||
if self.__check_all_combinations_in_ranges(list_of_ranges,
|
|
||||||
sigma_or_sign,
|
sigma_or_sign,
|
||||||
print_results=print_results):
|
print_results=print_results):
|
||||||
return True
|
return True
|
||||||
@ -781,12 +797,12 @@ TorusCable.get_number_of_combinations_of_theta.__doc__ = \
|
|||||||
and q_j is the last q parameter for the component (a single cable)
|
and q_j is the last q parameter for the component (a single cable)
|
||||||
"""
|
"""
|
||||||
|
|
||||||
TorusCable.set_knot_descrption.__doc__ = \
|
TorusCable.get_knot_descrption.__doc__ = \
|
||||||
"""
|
"""
|
||||||
Arguments:
|
Arguments:
|
||||||
arbitrary number of lists of numbers, each list encodes a single cable.
|
arbitrary number of lists of numbers, each list encodes a single cable.
|
||||||
Examples:
|
Examples:
|
||||||
sage: set_knot_descrption([1, 3], [2], [-1, -2], [-3])
|
sage: get_knot_descrption([1, 3], [2], [-1, -2], [-3])
|
||||||
'T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)'
|
'T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)'
|
||||||
"""
|
"""
|
||||||
|
|
||||||
|
|||||||
Loading…
Reference in New Issue
Block a user