Fix bug in WordMorphism.growing_letters() and periodic_points()

[mrejmon]

sage: WordMorphism('a->a').is_growing('a')
True

should return False.

This happens due to the if self.is_primitive(): return True optimization. Easily fixable for example like this:

-       if self.is_primitive():
+       if self.is_primitive() and len(self._morph) > 1:
            return True

sage: WordMorphism('a->a,b->bb').periodic_points()
Traceback (most recent call last):
...
ValueError: generator already executing

should return [[word: bbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbbb...]].

I think this happens because periodic_points() doesn't check whether the letters are growing, so the following should fix it (assuming we only care about periodic points with infinite length):

        A = self.domain().alphabet()
        d = dict((letter,self(letter)[0]) for letter in A)
+       G = set(self.growing_letters())

        res = []
        parent = self.codomain().shift()
        for cycle in get_cycles(CallableDict(d),A):
+           if cycle[0] in G:
                P = PeriodicPointIterator(self, cycle)
                res.append([parent(P._cache[i]) for i in range(len(cycle))])

I added a branch with the proposed fixes.

CC: @seblabbe @slel

Component: combinatorics

Author: Martin Rejmon

Branch/Commit: 87a8aae

Reviewer: Vincent Delecroix

Issue created by migration from https://trac.sagemath.org/ticket/31454

[seblabbe]

comment:3

Thanks for proposing such fixes. I will take a look as soon as possible.

[videlec]

comment:4

Martin. Your branch should include the two doctests that are in the ticket description. Since the sage doctests are run it will prevent the bug to occur again in the future.

[sagetrac-git]

Branch pushed to git repo; I updated commit sha1. New commits:

87a8aae

Add regression tests

[sagetrac-git]

Changed commit from 085165a to 87a8aae

[mrejmon]

comment:6

Replying to @videlec:

Martin. Your branch should include the two doctests that are in the ticket description. Since the sage doctests are run it will prevent the bug to occur again in the future.

Done.

[videlec]

Reviewer: Vincent Delecroix

[videlec]

comment:7

thanks!

[vbraun]

Changed branch from u/gh-mrejmon/fix_growing_and_periodic to 87a8aae