bugged stringlengths 4 228k | fixed stringlengths 0 96.3M | __index_level_0__ int64 0 481k |
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def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | 473,000 |
def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | def frequency_table(string): r""" Return the frequency table corresponding to the given string. INPUT: - ``string`` -- a string EXAMPLE:: sage: from sage.coding.source_coding.huffman import frequency_table sage: str = "Sage is my most favorite general purpose computer algebra system" sage: frequency_table(str) {'a'... | 473,001 |
def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 473,002 |
def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 473,003 |
def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 473,004 |
def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | def __init__(self, string = None, frequencies = None): r""" Constructor for Huffman | 473,005 |
def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 473,006 |
def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 473,007 |
def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | def _build_code_from_tree(self, tree, d, prefix=''): r""" Builds the code corresponding to a given tree and prefix | 473,008 |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 473,009 |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | def_build_code(self,dic):r"""ReturnsaHuffmancodeforeachoneofthegivenelements. | 473,010 |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 473,011 |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 473,012 |
def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | def _build_code(self, dic): r""" Returns a Huffman code for each one of the given elements. | 473,013 |
def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | 473,014 |
def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | defencode(self,string):r"""Returnsanencodingofthegivenstringbasedonthecurrentencodingtable | 473,015 |
def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | def encode(self, string): r""" Returns an encoding of the given string based on the current encoding table | 473,016 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,017 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,018 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,019 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,020 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,021 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,022 |
def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | def decode(self, string): r""" Returns a decoded version of the given string corresponding to the current encoding table. | 473,023 |
def encoding_table(self): r""" Returns the current encoding table | def encoding_table(self): r""" Returns the current encoding table | 473,024 |
def encoding_table(self): r""" Returns the current encoding table | def encoding_table(self): r""" Returns the current encoding table | 473,025 |
def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | 473,026 |
def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | 473,027 |
def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | def tree(self): r""" Returns the Huffman tree corresponding to the current encoding | 473,028 |
def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | def _generate_edges(self, tree, parent="", bit=""): """ Generate the edges of the given Huffman tree. INPUT: - ``tree`` -- a Huffman binary tree. - ``parent`` -- (default: empty string) a parent vertex with exactly two children. - ``bit`` -- (default: empty string) the bit signifying either the left or right branch... | 473,029 |
def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = parent s = "".join([parent, bit]) try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | 473,030 |
def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | 473,031 |
def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | def _generate_edges(self, tree, father='', id=''): if father=='': u = 'root' else: u = father try: return self._generate_edges(tree[0], father=father+id, id='0') + \ self._generate_edges(tree[1], father=father+id, id='1') + \ ([(u, father+id)] if (father+id) != '' else []) | 473,032 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 473,033 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 473,034 |
def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | def steiner_tree(self,vertices, weighted = False): r""" Returns a tree of minimum weight connecting the given set of vertices. | 473,035 |
def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | 473,036 |
def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | def cnf(self, xi=None, yi=None, format=None): """ Return a representation of this S-Box in conjunctive normal form. | 473,037 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 473,038 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | deflocal_coordinates_at_nonweierstrass(self,P,prec=20,name='t'):"""Foranon-WeierstrasspointP=(a,b)onthehyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x-aisthelocalparameter. | 473,039 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 473,040 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 473,041 |
def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | def local_coordinates_at_nonweierstrass(self, P, prec = 20, name = 't'): """ For a non-Weierstrass point P = (a,b) on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x - a is the local parameter. | 473,042 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 473,043 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 473,044 |
def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | def local_coordinates_at_weierstrass(self, P, prec = 20, name = 't'): """ For a finite Weierstrass point on the hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = y is the local parameter. | 473,045 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | deflocal_coordinates_at_infinity(self,prec=20,name='t'):"""Forthegenusghyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x^g/yisthelocalparameteratinfinity | 473,046 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | deflocal_coordinates_at_infinity(self,prec=20,name='t'):"""Forthegenusghyperellipticcurvey^2=f(x),returns(x(t),y(t))suchthat(y(t))^2=f(x(t)),wheret=x^g/yisthelocalparameteratinfinity | 473,047 |
def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | def local_coordinates_at_infinity(self, prec = 20, name = 't'): """ For the genus g hyperelliptic curve y^2 = f(x), returns (x(t), y(t)) such that (y(t))^2 = f(x(t)), where t = x^g/y is the local parameter at infinity | 473,048 |
def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | 473,049 |
def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | def local_coord(self, P, prec = 20, name = 't'): """ If P is not infinity, calls the appropriate local_coordinates function. | 473,050 |
def super_categories(self): """ Returns a list of the immediate super categories of self. | def super_categories(self): """ Returns a list of the immediate super categories of self. | 473,051 |
def one(self): r""" Returns the one of the monoid, that is the unique neutral element for `*`. | def one(self): r""" Returns the one of the monoid, that is the unique neutral element for `*`. | 473,052 |
def one_element(self): r""" Backward compatibility alias for :meth:`self.one()`. | def one_element(self): r""" Backward compatibility alias for :meth:`self.one()`. | 473,053 |
def prod(self, args): r""" n-ary product | def prod(self, args): r""" n-ary product | 473,054 |
def prod(self, args): r""" n-ary product | defprod(self,args):r"""n-aryproduct | 473,055 |
def is_one(self): r""" Returns whether self is the one of the monoid | def is_one(self): r""" Returns whether self is the one of the monoid | 473,056 |
def __pow__(self, n): r""" INPUTS: - n: a non negative integer | def __pow__(self, n): r""" INPUTS: - n: a non negative integer | 473,057 |
def _pow_naive(self, n): r""" A naive implementation of __pow__ | def _pow_naive(self, n): r""" A naive implementation of __pow__ | 473,058 |
def _pow_naive(self, n): r""" A naive implementation of __pow__ | def _pow_naive(self, n): r""" A naive implementation of __pow__ | 473,059 |
def _pow_naive(self, n): r""" A naive implementation of __pow__ | def _pow_naive(self, n): r""" A naive implementation of __pow__ | 473,060 |
def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using the Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the point suitable for plotting using the Tachyon ray tracer. | 473,061 |
def obj_repr(self, render_params): """ Returns complete representation of the point as a sphere. | def obj_repr(self, render_params): """ Returns complete representation of the point as a sphere. | 473,062 |
def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using the Tachyon ray tracer. | def tachyon_repr(self, render_params): """ Returns representation of the line suitable for plotting using the Tachyon ray tracer. | 473,063 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 473,064 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 473,065 |
def _render_on_subplot(self, subplot): """ TESTS: | def _render_on_subplot(self, subplot): """ TESTS: | 473,066 |
def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | def contour_plot(f, xrange, yrange, **options): r""" ``contour_plot`` takes a function of two variables, `f(x,y)` and plots contour lines of the function over the specified ``xrange`` and ``yrange`` as demonstrated below. ``contour_plot(f, (xmin, xmax), (ymin, ymax), ...)`` INPUT: - ``f`` -- a function of two variab... | 473,067 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 473,068 |
def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | def region_plot(f, xrange, yrange, plot_points, incol, outcol, bordercol, borderstyle, borderwidth,**options): r""" ``region_plot`` takes a boolean function of two variables, `f(x,y)` and plots the region where f is True over the specified ``xrange`` and ``yrange`` as demonstrated below. ``region_plot(f, (xmin, xmax),... | 473,069 |
def row_stabilizer(self): """ Return the PermutationGroup corresponding to the row stabilizer of self. | def row_stabilizer(self): """ Return the PermutationGroup corresponding to the row stabilizer of self. | 473,070 |
def replace_parens(x): r""" A map from '(' to open_symbol and ')' to close_symbol and otherwise an error is raised. EXAMPLES:: sage: from sage.combinat.dyck_word import replace_parens sage: replace_parens('(') 1 sage: replace_parens(')') 0 sage: replace_parens(1) Traceback (most recent call last): ... ValueError """ ... | def replace_parens(x): r""" A map from ``'('`` to ``open_symbol`` and ``')'`` to ``close_symbol`` and otherwise an error is raised. The values of the constants ``open_symbol`` and ``close_symbol`` are subject to change. This is the inverse map of :func:`replace_symbols`. INPUT: - ``x`` -- either an opening or closing... | 473,071 |
def replace_symbols(x): r""" A map from open_symbol to '(' and close_symbol to ')' and otherwise an error is raised. EXAMPLES:: sage: from sage.combinat.dyck_word import replace_symbols sage: replace_symbols(1) '(' sage: replace_symbols(0) ')' sage: replace_symbols(3) Traceback (most recent call last): ... ValueError... | def replace_symbols(x): r""" A map from ``open_symbol`` to ``'('`` and ``close_symbol`` to ``')'`` and otherwise an error is raised. The values of the constants ``open_symbol`` and ``close_symbol`` are subject to change. This is the inverse map of :func:`replace_parens`. INPUT: - ``x`` -- either ``open_symbol`` or ``... | 473,072 |
def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete. EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyc... | 473,073 |
def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | def DyckWord(dw=None, noncrossing_partition=None): r""" Returns a Dyck word object or a head of a Dyck word object if the Dyck word is not complete EXAMPLES:: sage: dw = DyckWord([1, 0, 1, 0]); dw [1, 0, 1, 0] sage: print dw ()() sage: print dw.height() 1 sage: dw.to_noncrossing_partition() [[1], [2]] :: sage: Dyck... | 473,074 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 473,075 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 473,076 |
def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | def associated_parenthesis(self, pos): r""" report the position for the parenthesis that matches the one at position ``pos`` | 473,077 |
def to_noncrossing_partition(self): r""" Bijection of Biane from Dyck words to non crossing partitions Thanks to Mathieu Dutour for describing the bijection. | def to_noncrossing_partition(self): r""" Bijection of Biane from Dyck words to non-crossing partitions. Thanks to Mathieu Dutour for describing the bijection. | 473,078 |
def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | 473,079 |
def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | def to_tableau(self): r""" returns a standard tableau of length less than or equal to 2 with the size the same as the length of the list the standard tableau will be rectangular iff ``self`` is a complete Dyck word | 473,080 |
def a_statistic(self): """ Returns the a-statistic for the Dyck word correspond to the area of the Dyck path. | def a_statistic(self): """ Returns the a-statistic for the Dyck word correspond to the area of the Dyck path. | 473,081 |
def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | 473,082 |
def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | def b_statistic(self): r""" Returns the b-statistic for the Dyck word corresponding to the bounce statistic of the Dyck word. | 473,083 |
def list(self): """ Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. | def list(self): """ Returns a list of all the Dyck words with ``k1`` opening and ``k2`` closing parentheses. | 473,084 |
def __iter__(self): r""" Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. | def __iter__(self): r""" Returns an iterator for Dyck words with ``k1`` opening and ``k2`` closing parentheses. | 473,085 |
def from_noncrossing_partition(ncp): r""" converts a non-crossing partition to a Dyck word TESTS:: sage: DyckWord(noncrossing_partition=[[1,2]]) # indirect doctest [1, 1, 0, 0] sage: DyckWord(noncrossing_partition=[[1],[2]]) [1, 0, 1, 0] :: sage: dws = DyckWords(5).list() sage: ncps = map( lambda x: x.to_noncrossin... | def from_noncrossing_partition(ncp): r""" Converts a non-crossing partition to a Dyck word. TESTS:: sage: DyckWord(noncrossing_partition=[[1,2]]) # indirect doctest [1, 1, 0, 0] sage: DyckWord(noncrossing_partition=[[1],[2]]) [1, 0, 1, 0] :: sage: dws = DyckWords(5).list() sage: ncps = map( lambda x: x.to_noncrossi... | 473,086 |
def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | def eliminate_linear_variables(self, maxlength=3, skip=lambda lm,tail: False): """ Return a new system where "linear variables" are eliminated. | 473,087 |
def __mul__(self, other): r""" Calculate the product self * other. | def __mul__(self, other): r""" Calculate the product self * other. | 473,088 |
def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. | def order(self, *args, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. | 473,089 |
def order(self, *gens, **kwds): r""" Return the order with given ring generators in the maximal order of this number field. | def order(self, *gens, **kwds): r sage: K.<a> = NumberField(x^3 - 2) sage: ZZ[a] Order in Number Field in a0 with defining polynomial x^3 - 2 TESTS: We verify that trac sage: K.<a> = NumberField(x^4 + 4*x^2 + 2) sage: B = K.integral_basis() sage: K.order(*B) Order in Number Field in a with defining polynomial x^4 + ... | 473,090 |
def __init__(self): r""" The inverse of the hyperbolic secant function. | def __init__(self): r""" The inverse of the hyperbolic secant function. | 473,091 |
def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. | def eval(self, Vobj): r""" Evaluates the left hand side `A\vec{x}+b` on the given vertex/ray/line. | 473,092 |
def is_inequality(self): """ Returns True since this is, by construction, an inequality. | def is_inequality(self): """ Returns True since this is, by construction, an inequality. | 473,093 |
def interior_contains(self, Vobj): """ Tests whether the interior of the halfspace (excluding its boundary) defined by the inequality contains the given vertex/ray/line. | def interior_contains(self, Vobj): If you pass a vector, it is assumed to be the coordinate vector of a point:: sage: P = Polyhedron(vertices=[[1,1],[1,-1],[-1,1],[-1,-1]]) sage: p = vector(ZZ, [1,0] ) sage: [ ieq.interior_contains(p) for ieq in P.inequality_generator() ] [True, True, True, False] """ try: if Vobj.is... | 473,094 |
def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | def is_equation(self): """ Tests if this object is an equation. By construction, it must be. | 473,095 |
def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | def is_vertex(self): """ Tests if this object is a vertex. By construction it always is. | 473,096 |
def is_ray(self): """ Tests if this object is a ray. Always True by construction. | def is_ray(self): """ Tests if this object is a ray. Always True by construction. | 473,097 |
def is_line(self): """ Tests if the object is a line. By construction it must be. | def is_line(self): """ Tests if the object is a line. By construction it must be. | 473,098 |
def identity(self): """ Returns the identity projection. | def identity(self): """ Returns the identity projection. | 473,099 |
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