first lines for cab.update function
This commit is contained in:
Maria Marchwicka
parent
b729a4eeee
commit
acbf651697
@ -7,6 +7,8 @@ from typing import Iterable
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SIGNATURE = 0
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SIGMA = 1
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# 9.11 (9.8)
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# 9.15 (9.9)
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class SignatureFunction(object):
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@ -21,40 +23,57 @@ class SignatureFunction(object):
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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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counter2 = collections.Counter({ k : v 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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assert counter2 == counter
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self.cnt_signature_jumps = counter
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self.tikz_plot("bum.tex")
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def sum_of_absolute_values(self):
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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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return not any(self.cnt_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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items = self.cnt_signature_jumps.items()
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counter = collections.Counter({ (1 + 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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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((1/2 + jump_arg/2, jump))
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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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def 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.cnt_signature_jumps.items():
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if jump_arg < 1/2 and jump != 0:
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if jump_arg < 1/2:
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new_data.append((2 * jump_arg, jump))
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counter = collections.Counter()
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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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counter[2 * jump_arg] = jump
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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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def minus_square_root(self):
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# to read values for t^(1/2)
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items = self.cnt_signature_jumps.items()
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counter = collections.Counter()
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for jump_arg, jump in self.cnt_signature_jumps.items():
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if jump_arg >= 1/2 and jump != 0:
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if jump_arg >= 1/2:
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counter[mod_one(2 * jump_arg)] = jump
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counter2 = collections.Counter({ mod_one(2 * k) : v for k, v in items if k >= 1/2 })
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assert counter2 == counter
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return SignatureFunction(counter=counter)
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def is_big(self):
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@ -63,12 +82,7 @@ class SignatureFunction(object):
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items = sorted(self.cnt_signature_jumps.items())
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for arg, jump in items:
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current += 2 * jump
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msg = "current = " + str(current) + ", jump = " + str(jump)
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msg += "\n" + str(self(arg))
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result = [jump for jump_arg, jump in self.cnt_signature_jumps.items() if jump_arg < mod_one(arg)]
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msg += "\nresult = " + str(sum(result))
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msg += "\narg = " + str(arg)
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assert current == self(arg) + jump, msg
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assert current == self(arg) + jump
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if abs(current) > abs(max):
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max = current
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# if abs(max) > 9:
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@ -81,6 +95,7 @@ class SignatureFunction(object):
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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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sf = SignatureFunction(values=new_data)
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counter = collections.Counter({mod_one(k + shift) : v \
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for k,v in self.cnt_signature_jumps.items()})
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assert SignatureFunction(counter=counter) == \
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@ -128,18 +143,29 @@ class SignatureFunction(object):
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def total_sign_jump(self):
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# Total signature jump is the sum of all jumps.
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result = sum([j[1] for j in self.to_list()])
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assert result == sum(v for _, v in self.cnt_signature_jumps.items())
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return sum([j[1] for j in self.to_list()])
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def to_list(self):
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# Return signature jumps formated as a list
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assert sorted(self.cnt_signature_jumps.items(), key = lambda x: x[0]) == \
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sorted(self.cnt_signature_jumps.items())
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return sorted(self.cnt_signature_jumps.items(), key = lambda x: x[0])
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def step_function_data(self):
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# Transform the signature jump data to a format understandable
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# by the plot function.
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l = self.to_list()
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assert l == sorted(self.cnt_signature_jumps.items())
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vals = ([(d[0], sum(2 * j[1] for j in l[:l.index(d)+1])) for d in l] +
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[(0,self.cnt_signature_jumps[0]), (1,self.total_sign_jump())])
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print("step_function_data")
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print(vals)
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counter = copy(self.cnt_signature_jumps)
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counter[0] = self.cnt_signature_jumps[0]
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counter[1] = self.total_sign_jump()
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print(sorted(counter.items()))
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return vals
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def plot(self):
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@ -147,7 +173,7 @@ class SignatureFunction(object):
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plot_step_function(self.step_function_data())
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def tikz_plot(self, file_name):
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# Draw the graph of the signature and transform it into TiKz.
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# Draw the graph of the signature and transform it into TiKz.
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# header of the LaTeX file
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with open(file_name, "w") as output_file:
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@ -156,10 +182,12 @@ class SignatureFunction(object):
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output_file.write("\\begin{document}\n")
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output_file.write("\\begin{tikzpicture}\n")
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data = sorted(self.step_function_data())
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print("data")
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print(data)
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output_file.write(" \\datavisualization[scientific axes,visualize as smooth line,\n")
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output_file.write(" x axis={ticks={none,major={at={")
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output_file.write(", " + str(N(data[0][0],digits=4)) + " as \\(" + str(data[0][0]) + "\\)")
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for jump_arg,jump in data:
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for jump_arg, jump in data:
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output_file.write(", " + str(N(jump_arg,digits=4)) + " as \\(" + str(jump_arg) + "\\)")
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output_file.write("}}}}\n")
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output_file.write(" ]\n")
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@ -191,9 +219,28 @@ class TorusCable(object):
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self.q_vector = q_vector
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k = k_vector
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self.knot_sum = eval(knot_formula)
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self.knot_description = self.get_knot_descrption()
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self.knot_description = self.set_knot_descrption()
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self.__sigma_function = None
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# TBD property function
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self.signature_as_function_of_theta = 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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def update(self, other):
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# TBD knot_formula etc.
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number_of_summands = len(self.knot_sum)
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self.knot_description += " # " + other.knot_description
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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_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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@ -273,12 +320,18 @@ class TorusCable(object):
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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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# 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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@ -354,7 +407,7 @@ class TorusCable(object):
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return SignatureFunction(values=w)
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def get_knot_descrption(self):
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def set_knot_descrption(self):
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description = ""
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for knot in self.knot_sum:
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if knot[0] < 0:
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@ -728,12 +781,12 @@ TorusCable.get_number_of_combinations_of_theta.__doc__ = \
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and q_j is the last q parameter for the component (a single cable)
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"""
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TorusCable.get_knot_descrption.__doc__ = \
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TorusCable.set_knot_descrption.__doc__ = \
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"""
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Arguments:
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arbitrary number of lists of numbers, each list encodes a single cable.
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Examples:
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sage: get_knot_descrption([1, 3], [2], [-1, -2], [-3])
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sage: set_knot_descrption([1, 3], [2], [-1, -2], [-3])
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'T(2, 3; 2, 7) # T(2, 5) # -T(2, 3; 2, 5) # -T(2, 7)'
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"""
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@ -20,8 +20,16 @@ class Config(object):
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# knot_formula is a schema for knots which signature function
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# will be calculated
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self.knot_formula = "[[k[0], k[1], k[3]], [-k[1], -k[3]], \
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[k[2], k[3]], [-k[0], -k[2], -k[3]]]"
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self.knot_formula = "[[k[0], k[1], k[3]], " + \
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"[-k[1], -k[3]], " + \
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"[k[2], k[3]], " + \
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"[-k[0], -k[2], -k[3]]]"
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# self.knot_formula = "[[k[0], k[1], k[4]], [-k[1], -k[3]], \
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# [k[2], k[3]], [-k[0], -k[2], -k[4]]]"
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#
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#
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# self.knot_formula = "[[k[3]], [-k[3]], \
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# [k[3]], [-k[3]] ]"
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@ -42,10 +50,10 @@ class Config(object):
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self.start_shift = 0
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self.verbose = True
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self.verbose = False
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# self.verbose = False
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self.print_results = True
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self.print_results = False
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# self.print_results = 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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@ -102,7 +110,7 @@ def set_parameters(knot_formula, limit, verbose, print_results):
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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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vebose = config.verbose
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verbose = config.verbose
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if print_results is None:
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print_results = config.print_results
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return knot_formula, limit, verbose, print_results
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@ -127,9 +135,8 @@ def search_for_large_sigma_value(knot_formula=None, limit=None,
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for c in combinations:
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q = [P.unrank(i + config.start_shift) for i in c]
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if config.only_slice_candidates:
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if not (q[3] > 4 * q[2] and
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q[2] > 4 * q[1] and
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q[1] > 4 * q[0]):
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ratio = q[3] > 4 * q[2] and q[2] > 4 * q[1] and q[1] > 4 * q[0]
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if not ratio:
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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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@ -143,9 +150,6 @@ def search_for_large_sigma_value(knot_formula=None, limit=None,
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# searching for signature == 0
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def search_for_null_signature_value(knot_formula=None, limit=None,
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verbose=None, print_results=None):
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@ -154,6 +158,8 @@ def search_for_null_signature_value(knot_formula=None, limit=None,
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set_parameters(knot_formula, limit, verbose, print_results)
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k_vector_size = extract_max(knot_formula) + 1
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limit = max(limit, k_vector_size)
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combinations = it.combinations_with_replacement(range(1, limit + 1),
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k_vector_size)
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with open(config.f_results, 'w') as f_results:
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@ -202,11 +208,9 @@ def search_for_large_signature_value(knot_formula=None, limit=None,
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# iterate over q-vector
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for c in combinations:
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q = [P.unrank(i + config.start_shift) for i in c]
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q[3] = 79
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if config.only_slice_candidates:
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if not (q[3] > 4 * q[2] and
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q[2] > 4 * q[1] and
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q[1] > 4 * q[0]):
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ratio = q[3] > 4 * q[2] and q[2] > 4 * q[1] and q[1] > 4 * q[0]
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if not ratio:
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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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