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r""" 

Infinite word 

 

AUTHORS: 

 

- Sebastien Labbe 

- Franco Saliola 

 

EXAMPLES: 

 

============================ 

Creation of an infinite word 

============================ 

 

Periodic infinite words:: 

 

sage: v = Word([0, 4, 8, 8, 3]) 

sage: vv = v^Infinity 

sage: vv 

word: 0488304883048830488304883048830488304883... 

 

Infinite words from a function `f:\mathbb{N}\rightarrow A` 

over an alphabet `A`:: 

 

sage: Word(lambda n: n%3) 

word: 0120120120120120120120120120120120120120... 

 

:: 

 

sage: def t(n): 

....: return add(Integer(n).digits(base=2)) % 2 

sage: Word(t, alphabet = [0, 1]) 

word: 0110100110010110100101100110100110010110... 

 

or as a one-liner:: 

 

sage: Word(lambda n : add(Integer(n).digits(base=2)) % 2, alphabet = [0, 1]) 

word: 0110100110010110100101100110100110010110... 

 

Infinite words from iterators:: 

 

sage: from itertools import count,repeat 

sage: Word( repeat(4) ) 

word: 4444444444444444444444444444444444444444... 

sage: Word( count() ) 

word: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,... 

 

Infinite words from morphism 

 

For example, let `A=\{a,b\}` and `\mu : A^* \rightarrow A^*` 

be the morphism defined by `a\mapsto ab, b\mapsto ba`:: 

 

sage: mu = WordMorphism('a->ab,b->ba'); mu 

WordMorphism: a->ab, b->ba 

sage: mu.fixed_point('a') 

word: abbabaabbaababbabaababbaabbabaabbaababba... 

 

Infinite words in a specific combinatorial class:: 

 

sage: W = InfiniteWords("ab"); W 

Infinite words over {'a', 'b'} 

sage: f = lambda n : 'a' if n % 2 == 1 else 'b' 

sage: W(f) 

word: babababababababababababababababababababa... 

""" 

#***************************************************************************** 

# Copyright (C) 2008 Sebastien Labbe <slabqc@gmail.com>, 

# Franco Saliola <saliola@gmail.com> 

# 

# This program is free software: you can redistribute it and/or modify 

# it under the terms of the GNU General Public License as published by 

# the Free Software Foundation, either version 2 of the License, or 

# (at your option) any later version. 

# http://www.gnu.org/licenses/ 

#***************************************************************************** 

from sage.combinat.words.abstract_word import Word_class 

from sage.combinat.words.word_options import word_options 

from sage.rings.all import Infinity 

 

class InfiniteWord_class(Word_class): 

def _repr_(self): 

r""" 

Returns a string representation of self. 

 

TESTS:: 

 

sage: Word(iter([1,2,3]), length="unknown")._repr_() 

'word: 123' 

sage: Word(range(100), length="unknown")._repr_() 

'word: 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,...' 

sage: Word(lambda x:x%3)._repr_() 

'word: 0120120120120120120120120120120120120120...' 

""" 

global word_options 

if word_options['old_repr']: 

return "Infinite word over %s"% str(self.parent().alphabet())[17:] 

return word_options['identifier'] + self.string_rep() 

 

def length(self): 

r""" 

Returns the length of self. 

 

EXAMPLES:: 

 

sage: f = lambda n : n % 6 

sage: w = Word(f); w 

word: 0123450123450123450123450123450123450123... 

sage: w.length() 

+Infinity 

""" 

return Infinity