Fast word datatype using an array of unsigned char¶
- class sage.combinat.words.word_char.WordDatatype_char[source]¶
- Bases: - WordDatatype- A Fast class for words represented by an array - unsigned char *.- Currently, only handles letters in [0,255]. - concatenate(other)[source]¶
- Concatenation of - selfand- other.- EXAMPLES: - sage: W = Words([0,1,2]) sage: W([0,2,1]).concatenate([0,0,0]) word: 021000 - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> W([Integer(0),Integer(2),Integer(1)]).concatenate([Integer(0),Integer(0),Integer(0)]) word: 021000 
 - has_prefix(other)[source]¶
- Test whether - otheris a prefix of- self.- INPUT: - other– a word or a sequence (e.g. tuple, list)
 - EXAMPLES: - sage: W = Words([0,1,2]) sage: w = W([0,1,1,0,1,2,0]) sage: w.has_prefix([0,1,1]) True sage: w.has_prefix([0,1,2]) False sage: w.has_prefix(w) True sage: w.has_prefix(w[:-1]) True sage: w.has_prefix(w[1:]) False - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> w = W([Integer(0),Integer(1),Integer(1),Integer(0),Integer(1),Integer(2),Integer(0)]) >>> w.has_prefix([Integer(0),Integer(1),Integer(1)]) True >>> w.has_prefix([Integer(0),Integer(1),Integer(2)]) False >>> w.has_prefix(w) True >>> w.has_prefix(w[:-Integer(1)]) True >>> w.has_prefix(w[Integer(1):]) False 
 - is_empty()[source]¶
- Return whether the word is empty. - EXAMPLES: - sage: W = Words([0,1,2]) sage: W([0,1,2,2]).is_empty() False sage: W([]).is_empty() True - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> W([Integer(0),Integer(1),Integer(2),Integer(2)]).is_empty() False >>> W([]).is_empty() True 
 - is_square()[source]¶
- Return - Trueif- selfis a square, and- Falseotherwise.- EXAMPLES: - sage: w = Word([n % 4 for n in range(48)], alphabet=[0,1,2,3]) sage: w.is_square() True - >>> from sage.all import * >>> w = Word([n % Integer(4) for n in range(Integer(48))], alphabet=[Integer(0),Integer(1),Integer(2),Integer(3)]) >>> w.is_square() True - sage: w = Word([n % 4 for n in range(49)], alphabet=[0,1,2,3]) sage: w.is_square() False sage: (w*w).is_square() True - >>> from sage.all import * >>> w = Word([n % Integer(4) for n in range(Integer(49))], alphabet=[Integer(0),Integer(1),Integer(2),Integer(3)]) >>> w.is_square() False >>> (w*w).is_square() True 
 - length()[source]¶
- Return the length of the word as a Sage integer. - EXAMPLES: - sage: W = Words([0,1,2,3,4]) sage: w = W([0,1,2,0,3,2,1]) sage: w.length() 7 sage: type(w.length()) <class 'sage.rings.integer.Integer'> sage: type(len(w)) <class 'int'> - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2),Integer(3),Integer(4)]) >>> w = W([Integer(0),Integer(1),Integer(2),Integer(0),Integer(3),Integer(2),Integer(1)]) >>> w.length() 7 >>> type(w.length()) <class 'sage.rings.integer.Integer'> >>> type(len(w)) <class 'int'> 
 - letters()[source]¶
- Return the list of letters that appear in this word, listed in the order of first appearance. - EXAMPLES: - sage: W = Words(5) sage: W([1,3,1,2,2,3,1]).letters() [1, 3, 2] - >>> from sage.all import * >>> W = Words(Integer(5)) >>> W([Integer(1),Integer(3),Integer(1),Integer(2),Integer(2),Integer(3),Integer(1)]).letters() [1, 3, 2] 
 - longest_common_prefix(other)[source]¶
- Return the longest common prefix of this word and - other.- EXAMPLES: - sage: W = Words([0,1,2]) sage: W([0,1,0,2]).longest_common_prefix([0,1]) word: 01 sage: u = W([0,1,0,0,1]) sage: v = W([0,1,0,2]) sage: u.longest_common_prefix(v) word: 010 sage: v.longest_common_prefix(u) word: 010 - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> W([Integer(0),Integer(1),Integer(0),Integer(2)]).longest_common_prefix([Integer(0),Integer(1)]) word: 01 >>> u = W([Integer(0),Integer(1),Integer(0),Integer(0),Integer(1)]) >>> v = W([Integer(0),Integer(1),Integer(0),Integer(2)]) >>> u.longest_common_prefix(v) word: 010 >>> v.longest_common_prefix(u) word: 010 - Using infinite words is also possible (and the return type is also a of the same type as - self):- sage: W([0,1,0,0]).longest_common_prefix(words.FibonacciWord()) word: 0100 sage: type(_) <class 'sage.combinat.words.word.FiniteWord_char'> - >>> from sage.all import * >>> W([Integer(0),Integer(1),Integer(0),Integer(0)]).longest_common_prefix(words.FibonacciWord()) word: 0100 >>> type(_) <class 'sage.combinat.words.word.FiniteWord_char'> - An example of an intensive usage: - sage: W = Words([0,1]) sage: w = words.FibonacciWord() sage: w = W(list(w[:5000])) sage: L = [[len(w[n:].longest_common_prefix(w[n+fibonacci(i):])) # needs sage.libs.pari ....: for i in range(5,15)] for n in range(1,1000)] sage: for n,l in enumerate(L): # needs sage.libs.pari ....: if l.count(0) > 4: ....: print("{} {}".format(n+1,l)) 375 [0, 13, 0, 34, 0, 89, 0, 233, 0, 233] 376 [0, 12, 0, 33, 0, 88, 0, 232, 0, 232] 608 [8, 0, 21, 0, 55, 0, 144, 0, 377, 0] 609 [7, 0, 20, 0, 54, 0, 143, 0, 376, 0] 985 [0, 13, 0, 34, 0, 89, 0, 233, 0, 610] 986 [0, 12, 0, 33, 0, 88, 0, 232, 0, 609] - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1)]) >>> w = words.FibonacciWord() >>> w = W(list(w[:Integer(5000)])) >>> L = [[len(w[n:].longest_common_prefix(w[n+fibonacci(i):])) # needs sage.libs.pari ... for i in range(Integer(5),Integer(15))] for n in range(Integer(1),Integer(1000))] >>> for n,l in enumerate(L): # needs sage.libs.pari ... if l.count(Integer(0)) > Integer(4): ... print("{} {}".format(n+Integer(1),l)) 375 [0, 13, 0, 34, 0, 89, 0, 233, 0, 233] 376 [0, 12, 0, 33, 0, 88, 0, 232, 0, 232] 608 [8, 0, 21, 0, 55, 0, 144, 0, 377, 0] 609 [7, 0, 20, 0, 54, 0, 143, 0, 376, 0] 985 [0, 13, 0, 34, 0, 89, 0, 233, 0, 610] 986 [0, 12, 0, 33, 0, 88, 0, 232, 0, 609] 
 - longest_common_suffix(other)[source]¶
- Return the longest common suffix between this word and - other.- EXAMPLES: - sage: W = Words([0,1,2]) sage: W([0,1,0,2]).longest_common_suffix([2,0,2]) word: 02 sage: u = W([0,1,0,0,1]) sage: v = W([1,2,0,0,1]) sage: u.longest_common_suffix(v) word: 001 sage: v.longest_common_suffix(u) word: 001 - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> W([Integer(0),Integer(1),Integer(0),Integer(2)]).longest_common_suffix([Integer(2),Integer(0),Integer(2)]) word: 02 >>> u = W([Integer(0),Integer(1),Integer(0),Integer(0),Integer(1)]) >>> v = W([Integer(1),Integer(2),Integer(0),Integer(0),Integer(1)]) >>> u.longest_common_suffix(v) word: 001 >>> v.longest_common_suffix(u) word: 001 
 
- sage.combinat.words.word_char.reversed_word_iterator(w)[source]¶
- This function exists only because it is not possible to use yield in the special method - __reversed__.- EXAMPLES: - sage: W = Words([0,1,2]) sage: w = W([0,1,0,0,1,2]) sage: list(reversed(w)) # indirect doctest [2, 1, 0, 0, 1, 0] - >>> from sage.all import * >>> W = Words([Integer(0),Integer(1),Integer(2)]) >>> w = W([Integer(0),Integer(1),Integer(0),Integer(0),Integer(1),Integer(2)]) >>> list(reversed(w)) # indirect doctest [2, 1, 0, 0, 1, 0]