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Issue 20405: Let (indexed) monoids know they are finitely generated

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Right now, free (indexed) monoids do not know they are finitely generated (when the index set is finite of course), meaning that they cannot use the generic iteration. We fix this here.

Depends on #20403

CC: @sagetrac-sage-combinat @nthiery

Component: categories

Author: Travis Scrimshaw

Branch/Commit: 740cf79

Reviewer: Julian Rüth

Issue created by migration from https://trac.sagemath.org/ticket/20405


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ee0536eAdded (indexed) monoids to finitely generated monoids category.

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

c95e024Fixing trivial failing doctests due to new iterator.

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

e640249Last fix of doctests.

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Dependencies: #20403


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Changed commit from e640249 to e7914d4


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

a0307f3Changed iterator for finitely generated semigroups.
c427ca9Change TODO list in backtrack to state we can deprecate TransitiveIdeal* now.
a27f383trac #20403 fixing one doctest
c20562etrac #20403 doc formatting
1c07d56Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' of trac.sagemath.org:sage into public/monoids/free_monoids_finitely_generated-20405
e7914d4Pulling changes from #17039 to fix doctest with this (#20405) + #20403.

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Branch pushed to git repo; I updated commit sha1. Last 10 new commits:

b07dfe2Doc of the two implementationsof ActiveTaskCounter
beebcbc#13580: Added comment on timing in the doc
58eca2e#13580: Removed comment which is now in the doc
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6272efdRemoving tab character.
740cf79Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' into public/monoids/free_monoids_finitely_generated-20405

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Reviewer: Julian Rüth


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comment:7

One patchbot complains about startup time. Another one is fine with it and I do not see how this could cause an increased startup time.


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Changed branch from public/monoids/free_monoids_finitely_generated-20405 to 740cf79


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