Comparison of combinatorial class of words with word paths is broken

[seblabbe]

This is fine :

sage: m = WordMorphism('a->adab,b->ab,c->cbcd,d->cd')
sage: m.is_endomorphism()
True

But we would like the following to be an endomorphism as well:

sage: P = WordPaths('abcd')
sage: m = WordMorphism('a->adab,b->ab,c->cbcd,d->cd', codomain=P)
sage: m.is_endomorphism()
False

It is caused by the following problem:

sage: WordPaths('abcd') <= Words('abcd')
False
sage: WordPaths('abcd') >= Words('abcd')
True
sage: Words('abcd') >= WordPaths('abcd')
False
sage: Words('abcd') <= WordPaths('abcd')
True

CC: @sagetrac-abmasse

Component: combinatorics

Author: Sébastien Labbé

Reviewer: Alexandre Blondin Massé

Merged: sage-4.6.1.alpha2

Issue created by migration from https://trac.sagemath.org/ticket/8674

[seblabbe]

Description changed:

--- 
+++ 
@@ -14,3 +14,16 @@
 sage: m.is_endomorphism()
 False
 ```
+
+It is caused by the following problem:
+
+```
+sage: WordPaths('abcd') <= Words('abcd')
+False
+sage: WordPaths('abcd') >= Words('abcd')
+True
+sage: Words('abcd') >= WordPaths('abcd')
+False
+sage: Words('abcd') <= WordPaths('abcd')
+True
+```

[seblabbe]

Does not depend on any known patch. Applies on 4.3.4.

[seblabbe]

comment:2

Attachment: trac_8674_word_combinaorial_cmp-sl.patch.gz

[sagetrac-abmasse]

comment:3

I understand that you want to correct the function is_endormorphism, but there is something strange about combinatorial class comparison.

For instance, I get the following:

sage: Words('ab') == WordPaths('ab')
False
sage: Words('ab') <= WordPaths('ab')
True
sage: Words('ab') >= WordPaths('ab')
False

Wouldn't we want

sage: Words('ab') == WordPaths('ab')
True

or is there something I miss ?

If it is a problem, maybe it's not necessary to fix the __eq__ operator now but do it in another ticket, but since you're at it...

[seblabbe]

Attachment: trac_8674_fixes_after_review-sl.patch.gz

Applies over the precedent patch

[seblabbe]

Author: Sébastien Labbé

[seblabbe]

Reviewer: Alexandre Blondin Massé