Owaner/CodeComputeX · Datasets at Hugging Face

code stringlengths 17 6.64M
class F_triangle(Triangle): '\n Class for the F-triangles.\n ' _prefix = 'F' def h(self): "\n Return the associated H-triangle.\n\n EXAMPLES::\n\n sage: from sage.combinat.triangles_FHM import F_triangle\n sage: x,y = polygens(ZZ,'x,y')\n sage:...
class Gamma_triangle(Triangle): '\n Class for the Gamma-triangles.\n ' _prefix = 'Γ' def h(self): "\n Return the associated H-triangle.\n\n The transition between Gamma-triangles and H-triangles is defined by\n\n .. MATH::\n\n H(x,y) = (1+x)^d \\sum_{0\\leq i...
class Tuples(Parent, UniqueRepresentation): '\n Return the enumerated set of ordered tuples of S of length k.\n\n An ordered tuple of length k of set is an ordered selection with\n repetition and is represented by a list of length k containing\n elements of set.\n\n EXAMPLES::\n\n sage: S = ...
class UnorderedTuples(Parent, UniqueRepresentation): '\n Return the enumerated set of unordered tuples of S of length k.\n\n An unordered tuple of length k of set is a unordered selection with\n repetitions of set and is represented by a sorted list of length k\n containing elements from set.\n\n E...
def find_min(vect): "\n Return a string of ``0``'s with one ``1`` at the location where the list\n ``vect`` has its last entry which is not equal to ``0``.\n\n INPUT:\n\n - ``vec`` -- A list of integers\n\n OUTPUT:\n\n A list of the same length with ``0``'s everywhere, except for a ``1``\n at...
def IntegerVectorsIterator(vect, min=None): '\n Return an iterator over the list of integer vectors which are componentwise\n less than or equal to ``vect``, and lexicographically greater than or equal\n to ``min``.\n\n INPUT:\n\n - ``vect`` -- A list of non-negative integers\n - ``min`` -- A li...
class VectorPartition(CombinatorialElement): '\n A vector partition is a multiset of integer vectors.\n ' @staticmethod def __classcall_private__(cls, vecpar): '\n Create a vector partition.\n\n EXAMPLES::\n\n sage: VectorPartition([[3, 2, 1], [2, 2, 1]])\n ...
class VectorPartitions(UniqueRepresentation, Parent): '\n Class of all vector partitions of ``vec`` with all parts greater than\n or equal to ``min`` in lexicographic order, with parts from ``parts``.\n\n A vector partition of ``vec`` is a list of vectors with non-negative\n integer entries whose sum ...
@richcmp_method class Word_class(SageObject): def parent(self): '\n Returns the parent of self.\n\n TESTS::\n\n sage: Word(iter([1,2,3]), length="unknown").parent()\n Finite words over Set of Python objects of class \'object\'\n sage: Word(range(12)).parent(...
def build_alphabet(data=None, names=None, name=None): '\n Return an object representing an ordered alphabet.\n\n INPUT:\n\n - ``data`` -- the letters of the alphabet; it can be:\n\n * a list/tuple/iterable of letters; the iterable may be infinite\n * an integer `n` to represent `\\{1, \\ldots, ...
class FiniteWord_class(Word_class): def __str__(self): '\n Return the full (not truncated) string representation of the word\n without identifier.\n\n TESTS::\n\n sage: Word(\'abc\').__str__()\n \'abc\'\n sage: Word([0, 1, 0, 0, 1] * 10).__str__()\n ...
class CallableFromListOfWords(tuple): '\n A class to create a callable from a list of words. The concatenation of\n a list of words is obtained by creating a word from this callable.\n ' def __new__(cls, words): '\n TESTS::\n\n sage: from sage.combinat.words.finite_word imp...
class Factorization(list): '\n A list subclass having a nicer representation for factorization of words.\n\n TESTS::\n\n sage: f = sage.combinat.words.finite_word.Factorization()\n sage: f == loads(dumps(f))\n True\n ' def __repr__(self): "\n Return a string repre...
def evaluation_dict(w): "\n Return a dictionary keyed by the letters occurring in ``w`` with\n values the number of occurrences of the letter.\n\n INPUT:\n\n - ``w`` -- a word\n\n TESTS::\n\n sage: from sage.combinat.words.finite_word import evaluation_dict\n sage: evaluation_dict([2,...
def word_to_ordered_set_partition(w): '\n Return the ordered set partition corresponding to a finite\n word `w`.\n\n If `w` is a finite word of length `n`, then the corresponding\n ordered set partition is an ordered set partition\n `(P_1, P_2, \\ldots, P_k)` of `\\{1, 2, \\ldots, n\\}`, where\n ...
class InfiniteWord_class(Word_class): def _repr_(self): '\n Returns a string representation of self.\n\n TESTS::\n\n sage: Word(iter([1,2,3]), length="unknown")._repr_()\n \'word: 123\'\n sage: Word(range(100), length="unknown")._repr_()\n \'word:...
def LyndonWords(e=None, k=None): '\n Return the combinatorial class of Lyndon words.\n\n A Lyndon word `w` is a word that is lexicographically less than all of\n its rotations. Equivalently, whenever `w` is split into two non-empty\n substrings, `w` is lexicographically less than the right substring....
def LyndonWord(data, check=True): '\n Construction of a Lyndon word.\n\n INPUT:\n\n - ``data`` -- list\n - ``check`` -- bool (optional, default: ``True``) if ``True``,\n check that the input data represents a Lyndon word.\n\n OUTPUT:\n\n A Lyndon word.\n\n EXAMPLES::\n\n sage: Lyn...
class LyndonWords_class(UniqueRepresentation, Parent): '\n The set of all Lyndon words.\n ' def __init__(self, alphabet=None): '\n INPUT:\n\n - ``alphabet`` -- the underlying alphabet\n\n TESTS::\n\n sage: loads(dumps(LyndonWords())) is LyndonWords()\n ...
class LyndonWords_evaluation(UniqueRepresentation, Parent): '\n The set of Lyndon words on a fixed multiset of letters.\n\n EXAMPLES::\n\n sage: L = LyndonWords([1,2,1])\n sage: L\n Lyndon words with evaluation [1, 2, 1]\n sage: L.list()\n [word: 1223, word: 1232, word: 13...
class LyndonWords_nk(UniqueRepresentation, Parent): '\n Lyndon words of fixed length `k` over the alphabet `\\{1, 2, \\ldots, n\\}`.\n\n INPUT:\n\n - ``n`` -- the size of the alphabet\n - ``k`` -- the length of the words\n\n EXAMPLES::\n\n sage: L = LyndonWords(3, 4)\n sage: L.list()\...
def StandardBracketedLyndonWords(n, k): '\n Return the combinatorial class of standard bracketed Lyndon words\n from [1, ..., n] of length k.\n\n These are in one to one correspondence with the Lyndon words and\n form a basis for the subspace of degree k of the free Lie algebra\n of rank n.\n\n ...
class StandardBracketedLyndonWords_nk(UniqueRepresentation, Parent): def __init__(self, n, k): '\n TESTS::\n\n sage: SBLW = StandardBracketedLyndonWords(3, 2)\n sage: SBLW == loads(dumps(SBLW))\n True\n ' self._n = n self._k = k self....
def standard_bracketing(lw): '\n Return the standard bracketing of a Lyndon word ``lw``.\n\n EXAMPLES::\n\n sage: import sage.combinat.words.lyndon_word as lyndon_word\n sage: [lyndon_word.standard_bracketing(u) for u in LyndonWords(3,3)]\n [[1, [1, 2]],\n [1, [1, 3]],\n ...
def standard_unbracketing(sblw): "\n Return flattened ``sblw`` if it is a standard bracketing of a Lyndon word,\n otherwise raise an error.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.lyndon_word import standard_unbracketing\n sage: standard_unbracketing([1, [2, 3]])\n word: 12...
class WordDatatype_morphic(WordDatatype_callable): '\n Datatype for a morphic word defined by a morphism, a starting letter\n and a coding.\n ' def __init__(self, parent, morphism, letter, coding=None, length=Infinity): '\n INPUT:\n\n - ``parent`` - a parent\n - ``morphi...
def get_cycles(f, domain): "\n Return the list of cycles of the function ``f`` contained in ``domain``.\n\n INPUT:\n\n - ``f`` - function.\n\n - ``domain`` - iterable, a subdomain of the domain of definition of ``f``.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.morphism import get_cycl...
class PeriodicPointIterator(): "\n (Lazy) constructor of the periodic points of a word morphism.\n\n This class is mainly used in :class:`WordMorphism.periodic_point` and\n :class:`WordMorphism.periodic_points`.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.morphism import PeriodicPointIter...
class WordMorphism(SageObject): "\n WordMorphism class\n\n INPUT:\n\n - ``data`` -- dict or str or an instance of WordMorphism, the map\n giving the image of letters\n - ``domain`` -- (optional:``None``) set of words over a given\n alphabet. If ``None``, the domain alphabet is computed from ...
def WordPaths(alphabet, steps=None): "\n Returns the combinatorial class of paths of the given type of steps.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet\n\n - ``steps`` - (default is None). It can be one of the following:\n\n - an iterable ordered container of as many vectors as there are\n...
class WordPaths_all(FiniteWords): '\n The combinatorial class of all paths, i.e of all words over\n an alphabet where each letter is mapped to a step (a vector).\n ' def __init__(self, alphabet, steps): "\n INPUT:\n\n - ``alphabet`` - an ordered alphabet\n\n - ``steps`` ...
class WordPaths_square_grid(WordPaths_all): '\n The combinatorial class of all paths on the square grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the square grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 4. The o...
class WordPaths_triangle_grid(WordPaths_all): '\n The combinatorial class of all paths on the triangle grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the triangle grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 6....
class WordPaths_hexagonal_grid(WordPaths_triangle_grid): '\n The combinatorial class of all paths on the hexagonal grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the hexagonal grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet...
class WordPaths_cube_grid(WordPaths_all): '\n The combinatorial class of all paths on the cube grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the cube grid.\n\n INPUT:\n\n - ``alphabet`` -- ordered alphabet of length 6. The order ...
class WordPaths_dyck(WordPaths_all): '\n The combinatorial class of all Dyck paths.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite Dyck paths.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 2. The order for the steps\n is : ...
class WordPaths_north_east(WordPaths_all): '\n The combinatorial class of all paths using North and East directions.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths using only north and east\n steps on the square grid.\n\n INPUT:\n\n ...
class FiniteWordPath_all(SageObject): def _repr_(self): "\n Returns a string representation of this path.\n\n EXAMPLES::\n\n sage: F = WordPaths('ab',[(1,0,0,0),(0,1,0,0)]); F\n Word Paths over 2 steps\n sage: f = F('ababab')\n sage: f._repr_()\n ...
class FiniteWordPath_2d(FiniteWordPath_all): def plot(self, pathoptions=dict(rgbcolor='red', thickness=3), fill=True, filloptions=dict(rgbcolor='red', alpha=0.2), startpoint=True, startoptions=dict(rgbcolor='red', pointsize=100), endarrow=True, arrowoptions=dict(rgbcolor='red', arrowsize=20, width=3), gridlines=...
class FiniteWordPath_3d(FiniteWordPath_all): def plot(self, pathoptions=dict(rgbcolor='red', arrow_head=True, thickness=3), startpoint=True, startoptions=dict(rgbcolor='red', size=10)): "\n INPUT:\n\n - ``pathoptions`` - (dict, default:dict(rgbcolor='red',arrow_head=True,\n thickne...
class FiniteWordPath_square_grid(FiniteWordPath_2d): def is_closed(self): "\n Returns True if self represents a closed path and False otherwise.\n\n EXAMPLES::\n\n sage: P = WordPaths('abAB', steps='square_grid')\n sage: P('aA').is_closed()\n True\n ...
class FiniteWordPath_triangle_grid(FiniteWordPath_2d): def xmin(self): "\n Returns the minimum of the x-coordinates of the path.\n\n EXAMPLES::\n\n sage: w = WordPaths('abcABC', steps='triangle')('ababcaaBC')\n sage: w.xmin()\n 0.000000000000000\n ...
class FiniteWordPath_hexagonal_grid(FiniteWordPath_triangle_grid): def __init__(self, parent, args, kwds): "\n INPUT:\n\n - ``parent`` - a parent object inheriting from Words_all\n that has the alphabet attribute defined\n\n - ``args, **kwds`` - arguments accepted by Abs...
class FiniteWordPath_cube_grid(FiniteWordPath_3d): pass
class FiniteWordPath_north_east(FiniteWordPath_2d): pass
class FiniteWordPath_dyck(FiniteWordPath_2d): pass
class FiniteWordPath_all_list(WordDatatype_list, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0,0),(3,4,0,0)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_list'...
class FiniteWordPath_all_str(WordDatatype_str, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab',[(1,2,0,0),(3,4,0,0)])\n sage: p = P('aabbb'); p\n Path: aabbb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_str'>\n ...
class FiniteWordPath_all_tuple(WordDatatype_tuple, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab',[(1,2,0,0),(3,4,0,0)])\n sage: p = P( ('a','b','b') ); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_tuple...
class FiniteWordPath_all_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_all, FiniteWord_class): pass
class FiniteWordPath_all_iter(WordDatatype_iter, FiniteWordPath_all, FiniteWord_class): pass
class FiniteWordPath_all_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_all, FiniteWord_class): pass
class FiniteWordPath_all_callable(WordDatatype_callable, FiniteWordPath_all, FiniteWord_class): pass
class FiniteWordPath_2d_list(WordDatatype_list, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_list'>\n ...
class FiniteWordPath_2d_str(WordDatatype_str, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P('aba'); p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_str'>\n sage: p ==...
class FiniteWordPath_2d_tuple(WordDatatype_tuple, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P(('a','b','a'));p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_tuple'>\n ...
class FiniteWordPath_2d_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_2d, FiniteWord_class): pass
class FiniteWordPath_2d_iter(WordDatatype_iter, FiniteWordPath_2d, FiniteWord_class): pass
class FiniteWordPath_2d_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_2d, FiniteWord_class): pass
class FiniteWordPath_2d_callable(WordDatatype_callable, FiniteWordPath_2d, FiniteWord_class): pass
class FiniteWordPath_3d_list(WordDatatype_list, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_list'>\n ...
class FiniteWordPath_3d_str(WordDatatype_str, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P('aba'); p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_str'>\n sage: ...
class FiniteWordPath_3d_tuple(WordDatatype_tuple, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P(('a','b','a'));p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_tuple'>\n ...
class FiniteWordPath_3d_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_3d, FiniteWord_class): pass
class FiniteWordPath_3d_iter(WordDatatype_iter, FiniteWordPath_3d, FiniteWord_class): pass
class FiniteWordPath_3d_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_3d, FiniteWord_class): pass
class FiniteWordPath_3d_callable(WordDatatype_callable, FiniteWordPath_3d, FiniteWord_class): pass
class FiniteWordPath_square_grid_list(WordDatatype_list, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_s...
class FiniteWordPath_square_grid_str(WordDatatype_str, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P('abccc'); p\n Path: abccc\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_square_...
class FiniteWordPath_square_grid_tuple(WordDatatype_tuple, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath...
class FiniteWordPath_square_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_square_grid, FiniteWord_class): pass
class FiniteWordPath_square_grid_iter(WordDatatype_iter, FiniteWordPath_square_grid, FiniteWord_class): pass
class FiniteWordPath_square_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_square_grid, FiniteWord_class): pass
class FiniteWordPath_square_grid_callable(WordDatatype_callable, FiniteWordPath_square_grid, FiniteWord_class): pass
class FiniteWordPath_triangle_grid_list(WordDatatype_list, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWo...
class FiniteWordPath_triangle_grid_str(WordDatatype_str, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_tri...
class FiniteWordPath_triangle_grid_tuple(WordDatatype_tuple, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.Finite...
class FiniteWordPath_triangle_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_triangle_grid, FiniteWord_class): pass
class FiniteWordPath_triangle_grid_iter(WordDatatype_iter, FiniteWordPath_triangle_grid, FiniteWord_class): pass
class FiniteWordPath_triangle_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_triangle_grid, FiniteWord_class): pass
class FiniteWordPath_triangle_grid_callable(WordDatatype_callable, FiniteWordPath_triangle_grid, FiniteWord_class): pass
class FiniteWordPath_hexagonal_grid_list(WordDatatype_list, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteW...
class FiniteWordPath_hexagonal_grid_str(WordDatatype_str, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_he...
class FiniteWordPath_hexagonal_grid_tuple(WordDatatype_tuple, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.Finit...
class FiniteWordPath_hexagonal_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass
class FiniteWordPath_hexagonal_grid_iter(WordDatatype_iter, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass
class FiniteWordPath_hexagonal_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass
class FiniteWordPath_hexagonal_grid_callable(WordDatatype_callable, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass
class FiniteWordPath_cube_grid_list(WordDatatype_list, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cube_...
class FiniteWordPath_cube_grid_str(WordDatatype_str, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cube_grid_str'>...
class FiniteWordPath_cube_grid_tuple(WordDatatype_tuple, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cub...
class FiniteWordPath_cube_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_cube_grid, FiniteWord_class): pass
class FiniteWordPath_cube_grid_iter(WordDatatype_iter, FiniteWordPath_cube_grid, FiniteWord_class): pass
class FiniteWordPath_cube_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_cube_grid, FiniteWord_class): pass
class FiniteWordPath_cube_grid_callable(WordDatatype_callable, FiniteWordPath_cube_grid, FiniteWord_class): pass
class FiniteWordPath_north_east_list(WordDatatype_list, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_eas...
class FiniteWordPath_north_east_str(WordDatatype_str, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_east_str'>\n ...
class FiniteWordPath_north_east_tuple(WordDatatype_tuple, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_e...
class FiniteWordPath_north_east_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_north_east, FiniteWord_class): pass
class FiniteWordPath_north_east_iter(WordDatatype_iter, FiniteWordPath_north_east, FiniteWord_class): pass

class F_triangle(Triangle): '\n Class for the F-triangles.\n ' _prefix = 'F' def h(self): "\n Return the associated H-triangle.\n\n EXAMPLES::\n\n sage: from sage.combinat.triangles_FHM import F_triangle\n sage: x,y = polygens(ZZ,'x,y')\n sage:...

class Gamma_triangle(Triangle): '\n Class for the Gamma-triangles.\n ' _prefix = 'Γ' def h(self): "\n Return the associated H-triangle.\n\n The transition between Gamma-triangles and H-triangles is defined by\n\n .. MATH::\n\n H(x,y) = (1+x)^d \\sum_{0\\leq i...

class Tuples(Parent, UniqueRepresentation): '\n Return the enumerated set of ordered tuples of S of length k.\n\n An ordered tuple of length k of set is an ordered selection with\n repetition and is represented by a list of length k containing\n elements of set.\n\n EXAMPLES::\n\n sage: S = ...

class UnorderedTuples(Parent, UniqueRepresentation): '\n Return the enumerated set of unordered tuples of S of length k.\n\n An unordered tuple of length k of set is a unordered selection with\n repetitions of set and is represented by a sorted list of length k\n containing elements from set.\n\n E...

def find_min(vect): "\n Return a string of ``0``'s with one ``1`` at the location where the list\n ``vect`` has its last entry which is not equal to ``0``.\n\n INPUT:\n\n - ``vec`` -- A list of integers\n\n OUTPUT:\n\n A list of the same length with ``0``'s everywhere, except for a ``1``\n at...

def IntegerVectorsIterator(vect, min=None): '\n Return an iterator over the list of integer vectors which are componentwise\n less than or equal to ``vect``, and lexicographically greater than or equal\n to ``min``.\n\n INPUT:\n\n - ``vect`` -- A list of non-negative integers\n - ``min`` -- A li...

class VectorPartition(CombinatorialElement): '\n A vector partition is a multiset of integer vectors.\n ' @staticmethod def __classcall_private__(cls, vecpar): '\n Create a vector partition.\n\n EXAMPLES::\n\n sage: VectorPartition([[3, 2, 1], [2, 2, 1]])\n ...

class VectorPartitions(UniqueRepresentation, Parent): '\n Class of all vector partitions of ``vec`` with all parts greater than\n or equal to ``min`` in lexicographic order, with parts from ``parts``.\n\n A vector partition of ``vec`` is a list of vectors with non-negative\n integer entries whose sum ...

@richcmp_method class Word_class(SageObject): def parent(self): '\n Returns the parent of self.\n\n TESTS::\n\n sage: Word(iter([1,2,3]), length="unknown").parent()\n Finite words over Set of Python objects of class \'object\'\n sage: Word(range(12)).parent(...

def build_alphabet(data=None, names=None, name=None): '\n Return an object representing an ordered alphabet.\n\n INPUT:\n\n - ``data`` -- the letters of the alphabet; it can be:\n\n * a list/tuple/iterable of letters; the iterable may be infinite\n * an integer `n` to represent `\\{1, \\ldots, ...

class FiniteWord_class(Word_class): def __str__(self): '\n Return the full (not truncated) string representation of the word\n without identifier.\n\n TESTS::\n\n sage: Word(\'abc\').__str__()\n \'abc\'\n sage: Word([0, 1, 0, 0, 1] * 10).__str__()\n ...

class CallableFromListOfWords(tuple): '\n A class to create a callable from a list of words. The concatenation of\n a list of words is obtained by creating a word from this callable.\n ' def __new__(cls, words): '\n TESTS::\n\n sage: from sage.combinat.words.finite_word imp...

class Factorization(list): '\n A list subclass having a nicer representation for factorization of words.\n\n TESTS::\n\n sage: f = sage.combinat.words.finite_word.Factorization()\n sage: f == loads(dumps(f))\n True\n ' def __repr__(self): "\n Return a string repre...

def evaluation_dict(w): "\n Return a dictionary keyed by the letters occurring in ``w`` with\n values the number of occurrences of the letter.\n\n INPUT:\n\n - ``w`` -- a word\n\n TESTS::\n\n sage: from sage.combinat.words.finite_word import evaluation_dict\n sage: evaluation_dict([2,...

def word_to_ordered_set_partition(w): '\n Return the ordered set partition corresponding to a finite\n word `w`.\n\n If `w` is a finite word of length `n`, then the corresponding\n ordered set partition is an ordered set partition\n `(P_1, P_2, \\ldots, P_k)` of `\\{1, 2, \\ldots, n\\}`, where\n ...

class InfiniteWord_class(Word_class): def _repr_(self): '\n Returns a string representation of self.\n\n TESTS::\n\n sage: Word(iter([1,2,3]), length="unknown")._repr_()\n \'word: 123\'\n sage: Word(range(100), length="unknown")._repr_()\n \'word:...

def LyndonWords(e=None, k=None): '\n Return the combinatorial class of Lyndon words.\n\n A Lyndon word `w` is a word that is lexicographically less than all of\n its rotations. Equivalently, whenever `w` is split into two non-empty\n substrings, `w` is lexicographically less than the right substring....

def LyndonWord(data, check=True): '\n Construction of a Lyndon word.\n\n INPUT:\n\n - ``data`` -- list\n - ``check`` -- bool (optional, default: ``True``) if ``True``,\n check that the input data represents a Lyndon word.\n\n OUTPUT:\n\n A Lyndon word.\n\n EXAMPLES::\n\n sage: Lyn...

class LyndonWords_class(UniqueRepresentation, Parent): '\n The set of all Lyndon words.\n ' def __init__(self, alphabet=None): '\n INPUT:\n\n - ``alphabet`` -- the underlying alphabet\n\n TESTS::\n\n sage: loads(dumps(LyndonWords())) is LyndonWords()\n ...

class LyndonWords_evaluation(UniqueRepresentation, Parent): '\n The set of Lyndon words on a fixed multiset of letters.\n\n EXAMPLES::\n\n sage: L = LyndonWords([1,2,1])\n sage: L\n Lyndon words with evaluation [1, 2, 1]\n sage: L.list()\n [word: 1223, word: 1232, word: 13...

class LyndonWords_nk(UniqueRepresentation, Parent): '\n Lyndon words of fixed length `k` over the alphabet `\\{1, 2, \\ldots, n\\}`.\n\n INPUT:\n\n - ``n`` -- the size of the alphabet\n - ``k`` -- the length of the words\n\n EXAMPLES::\n\n sage: L = LyndonWords(3, 4)\n sage: L.list()\...

def StandardBracketedLyndonWords(n, k): '\n Return the combinatorial class of standard bracketed Lyndon words\n from [1, ..., n] of length k.\n\n These are in one to one correspondence with the Lyndon words and\n form a basis for the subspace of degree k of the free Lie algebra\n of rank n.\n\n ...

class StandardBracketedLyndonWords_nk(UniqueRepresentation, Parent): def __init__(self, n, k): '\n TESTS::\n\n sage: SBLW = StandardBracketedLyndonWords(3, 2)\n sage: SBLW == loads(dumps(SBLW))\n True\n ' self._n = n self._k = k self....

def standard_bracketing(lw): '\n Return the standard bracketing of a Lyndon word ``lw``.\n\n EXAMPLES::\n\n sage: import sage.combinat.words.lyndon_word as lyndon_word\n sage: [lyndon_word.standard_bracketing(u) for u in LyndonWords(3,3)]\n [[1, [1, 2]],\n [1, [1, 3]],\n ...

def standard_unbracketing(sblw): "\n Return flattened ``sblw`` if it is a standard bracketing of a Lyndon word,\n otherwise raise an error.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.lyndon_word import standard_unbracketing\n sage: standard_unbracketing([1, [2, 3]])\n word: 12...

class WordDatatype_morphic(WordDatatype_callable): '\n Datatype for a morphic word defined by a morphism, a starting letter\n and a coding.\n ' def __init__(self, parent, morphism, letter, coding=None, length=Infinity): '\n INPUT:\n\n - ``parent`` - a parent\n - ``morphi...

def get_cycles(f, domain): "\n Return the list of cycles of the function ``f`` contained in ``domain``.\n\n INPUT:\n\n - ``f`` - function.\n\n - ``domain`` - iterable, a subdomain of the domain of definition of ``f``.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.morphism import get_cycl...

class PeriodicPointIterator(): "\n (Lazy) constructor of the periodic points of a word morphism.\n\n This class is mainly used in :class:`WordMorphism.periodic_point` and\n :class:`WordMorphism.periodic_points`.\n\n EXAMPLES::\n\n sage: from sage.combinat.words.morphism import PeriodicPointIter...

class WordMorphism(SageObject): "\n WordMorphism class\n\n INPUT:\n\n - ``data`` -- dict or str or an instance of WordMorphism, the map\n giving the image of letters\n - ``domain`` -- (optional:``None``) set of words over a given\n alphabet. If ``None``, the domain alphabet is computed from ...

def WordPaths(alphabet, steps=None): "\n Returns the combinatorial class of paths of the given type of steps.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet\n\n - ``steps`` - (default is None). It can be one of the following:\n\n - an iterable ordered container of as many vectors as there are\n...

class WordPaths_all(FiniteWords): '\n The combinatorial class of all paths, i.e of all words over\n an alphabet where each letter is mapped to a step (a vector).\n ' def __init__(self, alphabet, steps): "\n INPUT:\n\n - ``alphabet`` - an ordered alphabet\n\n - ``steps`` ...

class WordPaths_square_grid(WordPaths_all): '\n The combinatorial class of all paths on the square grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the square grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 4. The o...

class WordPaths_triangle_grid(WordPaths_all): '\n The combinatorial class of all paths on the triangle grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the triangle grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 6....

class WordPaths_hexagonal_grid(WordPaths_triangle_grid): '\n The combinatorial class of all paths on the hexagonal grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the hexagonal grid.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet...

class WordPaths_cube_grid(WordPaths_all): '\n The combinatorial class of all paths on the cube grid.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths on the cube grid.\n\n INPUT:\n\n - ``alphabet`` -- ordered alphabet of length 6. The order ...

class WordPaths_dyck(WordPaths_all): '\n The combinatorial class of all Dyck paths.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite Dyck paths.\n\n INPUT:\n\n - ``alphabet`` - ordered alphabet of length 2. The order for the steps\n is : ...

class WordPaths_north_east(WordPaths_all): '\n The combinatorial class of all paths using North and East directions.\n ' def __init__(self, alphabet): "\n The combinatorial class of all finite paths using only north and east\n steps on the square grid.\n\n INPUT:\n\n ...

class FiniteWordPath_all(SageObject): def _repr_(self): "\n Returns a string representation of this path.\n\n EXAMPLES::\n\n sage: F = WordPaths('ab',[(1,0,0,0),(0,1,0,0)]); F\n Word Paths over 2 steps\n sage: f = F('ababab')\n sage: f._repr_()\n ...

class FiniteWordPath_2d(FiniteWordPath_all): def plot(self, pathoptions=dict(rgbcolor='red', thickness=3), fill=True, filloptions=dict(rgbcolor='red', alpha=0.2), startpoint=True, startoptions=dict(rgbcolor='red', pointsize=100), endarrow=True, arrowoptions=dict(rgbcolor='red', arrowsize=20, width=3), gridlines=...

class FiniteWordPath_3d(FiniteWordPath_all): def plot(self, pathoptions=dict(rgbcolor='red', arrow_head=True, thickness=3), startpoint=True, startoptions=dict(rgbcolor='red', size=10)): "\n INPUT:\n\n - ``pathoptions`` - (dict, default:dict(rgbcolor='red',arrow_head=True,\n thickne...

class FiniteWordPath_square_grid(FiniteWordPath_2d): def is_closed(self): "\n Returns True if self represents a closed path and False otherwise.\n\n EXAMPLES::\n\n sage: P = WordPaths('abAB', steps='square_grid')\n sage: P('aA').is_closed()\n True\n ...

class FiniteWordPath_triangle_grid(FiniteWordPath_2d): def xmin(self): "\n Returns the minimum of the x-coordinates of the path.\n\n EXAMPLES::\n\n sage: w = WordPaths('abcABC', steps='triangle')('ababcaaBC')\n sage: w.xmin()\n 0.000000000000000\n ...

class FiniteWordPath_hexagonal_grid(FiniteWordPath_triangle_grid): def __init__(self, parent, *args, **kwds): "\n INPUT:\n\n - ``parent`` - a parent object inheriting from Words_all\n that has the alphabet attribute defined\n\n - ``*args, **kwds`` - arguments accepted by Abs...

class FiniteWordPath_cube_grid(FiniteWordPath_3d): pass

class FiniteWordPath_north_east(FiniteWordPath_2d): pass

class FiniteWordPath_dyck(FiniteWordPath_2d): pass

class FiniteWordPath_all_list(WordDatatype_list, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0,0),(3,4,0,0)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_list'...

class FiniteWordPath_all_str(WordDatatype_str, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab',[(1,2,0,0),(3,4,0,0)])\n sage: p = P('aabbb'); p\n Path: aabbb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_str'>\n ...

class FiniteWordPath_all_tuple(WordDatatype_tuple, FiniteWordPath_all, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab',[(1,2,0,0),(3,4,0,0)])\n sage: p = P( ('a','b','b') ); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_all_tuple...

class FiniteWordPath_all_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_all, FiniteWord_class): pass

class FiniteWordPath_all_iter(WordDatatype_iter, FiniteWordPath_all, FiniteWord_class): pass

class FiniteWordPath_all_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_all, FiniteWord_class): pass

class FiniteWordPath_all_callable(WordDatatype_callable, FiniteWordPath_all, FiniteWord_class): pass

class FiniteWordPath_2d_list(WordDatatype_list, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_list'>\n ...

class FiniteWordPath_2d_str(WordDatatype_str, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P('aba'); p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_str'>\n sage: p ==...

class FiniteWordPath_2d_tuple(WordDatatype_tuple, FiniteWordPath_2d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2),(3,4)])\n sage: p = P(('a','b','a'));p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_2d_tuple'>\n ...

class FiniteWordPath_2d_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_2d, FiniteWord_class): pass

class FiniteWordPath_2d_iter(WordDatatype_iter, FiniteWordPath_2d, FiniteWord_class): pass

class FiniteWordPath_2d_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_2d, FiniteWord_class): pass

class FiniteWordPath_2d_callable(WordDatatype_callable, FiniteWordPath_2d, FiniteWord_class): pass

class FiniteWordPath_3d_list(WordDatatype_list, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P(['a','b','a']);p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_list'>\n ...

class FiniteWordPath_3d_str(WordDatatype_str, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P('aba'); p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_str'>\n sage: ...

class FiniteWordPath_3d_tuple(WordDatatype_tuple, FiniteWordPath_3d, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths(['a','b'],[(1,2,0),(3,4,0)])\n sage: p = P(('a','b','a'));p\n Path: aba\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_3d_tuple'>\n ...

class FiniteWordPath_3d_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_3d, FiniteWord_class): pass

class FiniteWordPath_3d_iter(WordDatatype_iter, FiniteWordPath_3d, FiniteWord_class): pass

class FiniteWordPath_3d_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_3d, FiniteWord_class): pass

class FiniteWordPath_3d_callable(WordDatatype_callable, FiniteWordPath_3d, FiniteWord_class): pass

class FiniteWordPath_square_grid_list(WordDatatype_list, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_s...

class FiniteWordPath_square_grid_str(WordDatatype_str, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P('abccc'); p\n Path: abccc\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_square_...

class FiniteWordPath_square_grid_tuple(WordDatatype_tuple, FiniteWordPath_square_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcd', steps='square')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath...

class FiniteWordPath_square_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_square_grid, FiniteWord_class): pass

class FiniteWordPath_square_grid_iter(WordDatatype_iter, FiniteWordPath_square_grid, FiniteWord_class): pass

class FiniteWordPath_square_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_square_grid, FiniteWord_class): pass

class FiniteWordPath_square_grid_callable(WordDatatype_callable, FiniteWordPath_square_grid, FiniteWord_class): pass

class FiniteWordPath_triangle_grid_list(WordDatatype_list, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWo...

class FiniteWordPath_triangle_grid_str(WordDatatype_str, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_tri...

class FiniteWordPath_triangle_grid_tuple(WordDatatype_tuple, FiniteWordPath_triangle_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='triangle')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.Finite...

class FiniteWordPath_triangle_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_triangle_grid, FiniteWord_class): pass

class FiniteWordPath_triangle_grid_iter(WordDatatype_iter, FiniteWordPath_triangle_grid, FiniteWord_class): pass

class FiniteWordPath_triangle_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_triangle_grid, FiniteWord_class): pass

class FiniteWordPath_triangle_grid_callable(WordDatatype_callable, FiniteWordPath_triangle_grid, FiniteWord_class): pass

class FiniteWordPath_hexagonal_grid_list(WordDatatype_list, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteW...

class FiniteWordPath_hexagonal_grid_str(WordDatatype_str, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_he...

class FiniteWordPath_hexagonal_grid_tuple(WordDatatype_tuple, FiniteWordPath_hexagonal_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='hexagon')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.Finit...

class FiniteWordPath_hexagonal_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass

class FiniteWordPath_hexagonal_grid_iter(WordDatatype_iter, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass

class FiniteWordPath_hexagonal_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass

class FiniteWordPath_hexagonal_grid_callable(WordDatatype_callable, FiniteWordPath_hexagonal_grid, FiniteWord_class): pass

class FiniteWordPath_cube_grid_list(WordDatatype_list, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cube_...

class FiniteWordPath_cube_grid_str(WordDatatype_str, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cube_grid_str'>...

class FiniteWordPath_cube_grid_tuple(WordDatatype_tuple, FiniteWordPath_cube_grid, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('abcdef', steps='cube')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_cub...

class FiniteWordPath_cube_grid_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_cube_grid, FiniteWord_class): pass

class FiniteWordPath_cube_grid_iter(WordDatatype_iter, FiniteWordPath_cube_grid, FiniteWord_class): pass

class FiniteWordPath_cube_grid_callable_with_caching(WordDatatype_callable_with_caching, FiniteWordPath_cube_grid, FiniteWord_class): pass

class FiniteWordPath_cube_grid_callable(WordDatatype_callable, FiniteWordPath_cube_grid, FiniteWord_class): pass

class FiniteWordPath_north_east_list(WordDatatype_list, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P(['a','b','b']); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_eas...

class FiniteWordPath_north_east_str(WordDatatype_str, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P('abb'); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_east_str'>\n ...

class FiniteWordPath_north_east_tuple(WordDatatype_tuple, FiniteWordPath_north_east, FiniteWord_class): "\n TESTS::\n\n sage: P = WordPaths('ab', steps='ne')\n sage: p = P(('a','b','b')); p\n Path: abb\n sage: type(p)\n <class 'sage.combinat.words.paths.FiniteWordPath_north_e...

class FiniteWordPath_north_east_iter_with_caching(WordDatatype_iter_with_caching, FiniteWordPath_north_east, FiniteWord_class): pass

class FiniteWordPath_north_east_iter(WordDatatype_iter, FiniteWordPath_north_east, FiniteWord_class): pass