[with patch, positive review] Improve iterator of word morphisms

[slabbe]

Right now, we can iterate over word morphisms with specific image lengths :

    Iterator over morphisms with specific image lengths::

	sage: map(str, W.iter_morphisms([2, 1]))
	['WordMorphism: a->aa, b->a',
	 'WordMorphism: a->aa, b->b',
	 'WordMorphism: a->ab, b->a',
	 'WordMorphism: a->ab, b->b',
	 'WordMorphism: a->ba, b->a',
	 'WordMorphism: a->ba, b->b',
	 'WordMorphism: a->bb, b->a',
	 'WordMorphism: a->bb, b->b']
	sage: map(str, W.iter_morphisms([2, 2]))
	['WordMorphism: a->aa, b->aa',
	 'WordMorphism: a->aa, b->ab',
	 'WordMorphism: a->aa, b->ba',
	 'WordMorphism: a->aa, b->bb',
	 'WordMorphism: a->ab, b->aa',
	 'WordMorphism: a->ab, b->ab',
	 'WordMorphism: a->ab, b->ba',
	 'WordMorphism: a->ab, b->bb',
	 'WordMorphism: a->ba, b->aa',
	 'WordMorphism: a->ba, b->ab',
	 'WordMorphism: a->ba, b->ba',
	 'WordMorphism: a->ba, b->bb',
	 'WordMorphism: a->bb, b->aa',
	 'WordMorphism: a->bb, b->ab',
	 'WordMorphism: a->bb, b->ba',
	 'WordMorphism: a->bb, b->bb']
	sage: map(str, W.iter_morphisms([0, 0]))
	['WordMorphism: a->, b->']
	sage: map(str, W.iter_morphisms([0, 1]))
	['WordMorphism: a->, b->a', 'WordMorphism: a->, b->b']

I want to iterate over all (non erasing) morphisms! In particuliar, I want the following to work :

    sage: W = Words('ab')                 
    sage: it = W.iter_morphisms()
    sage: for _ in range(10): print it.next()
    WordMorphism: a->a, b->a
    WordMorphism: a->a, b->b
    WordMorphism: a->b, b->a
    WordMorphism: a->b, b->b
    WordMorphism: a->aa, b->a
    WordMorphism: a->aa, b->b
    WordMorphism: a->ab, b->a
    WordMorphism: a->ab, b->b
    WordMorphism: a->ba, b->a
    WordMorphism: a->ba, b->b

[slabbe]

There is a bug in my patch. Some tests are apparently failing....

[slabbe]

Failing tests were related to #5600 because the patch I first posted here was depending on compositions-cleanup-5600-nt.patch. The patch word_iter_morphism_6571-sl.patch should now apply cleanly (including doctests) on sage-4.1.1.alpha0.

[slabbe]

This file depends on #6519 as well as on #5600

[slabbe]

Since #5600 should be merge soon (it has a positive review), I just uploaded a new patch that uses the benefits of #5600.

[saliola]

I made a few changes:

1. As written, the iter_morphisms method is recursive if it is iterating through all morphisms (it calls self.iter_morphisms(composition) for all compositions). This is not necessary and it is inefficient. I changed the code to avoid doing this.

2. Switched from Compositions to IntegerListsLex instead: the patch converted compositions spit out by Compositions to lists; so I changed it because compositions are created from the lists output by IntegerListsLex.

3. IntegerListsLex allows one to specify min_part, so I added a min_length keyword option (so erasing morphisms can be obtained by taking min_length=0). The default is 1 (the current behaviour).

[saliola]

Apply on top of word_iter_morphism_6571-sl.patch

[saliola]

In case it matters: I applied the patches from #5600 before word_iter_morphism_6571-sl.patch.

[slabbe]

This patch applies over the precedent two.

[slabbe]

Thanks Franco for your good review. I didn't know about IntegerListsLex. Allowing erasing morphism is great as well. I just added a small patch to correct a word in a one-line comment. I am currently building the documentation...

[slabbe]

Applies over the precedent three patches.

[slabbe]

There was a bug in the ReST documentation. I just added trac_6571-ReST-bug.patch which corrects it. Documentation now builds without warnings. Doctests passed on words.py. I am giving a positive review to Franco's changes.

[saliola]

Sébastien's documentation changes are good.