Allow IndexedGenerators to handle `names`

[tscrim]

So we can do things like

sage: C.<x,y,z> = CombinatorialFreeModule(QQ)

[tscrim]

Done and up for review.

---

New commits:

​f94c3f8	Another optio for indexed generators.
​5b546c2	Fixed failing doctest.
​d23726c	Added support for C.<x,...> for CombinatorialFreeModule.

[git]

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

​06e7a3c

Merge branch 'public/misc/names_argument_indexed_generators-17039' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039

[git]

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

​1aae120

Merge branch 'public/misc/names_argument_indexed_generators-17039' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039

[git]

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

​7a387fa	Merge branch 'public/misc/names_argument_indexed_generators-17039' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039
​e3175db	Fixing doctest ordering.

[git]

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

​84792f6	Merge branch 'public/misc/names_argument_indexed_generators-17039' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039
​ee0536e	Added (indexed) monoids to finitely generated monoids category.
​63e54b0	Merge branch 'public/monoids/free_monoids_finitely_generated-20405' into public/misc/names_argument_indexed_generators-17039
​a0307f3	Changed iterator for finitely generated semigroups.
​c427ca9	Change TODO list in backtrack to state we can deprecate TransitiveIdeal* now.
​dfa5c75	Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' into public/misc/names_argument_indexed_generators-17039
​fc9a4f8	Being more python3 compatible.

[git]

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

​0c3452d	Changing behavior of _first_ngens to support using gens().
​c95e024	Fixing trivial failing doctests due to new iterator.
​52f7f98	Merge branch 'public/monoids/free_monoids_finitely_generated-20405' into public/misc/names_argument_indexed_generators-17039

[git]

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

​a27f383	trac #20403 fixing one doctest
​c20562e	trac #20403 doc formatting
​fabe683	Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039
​e640249	Last fix of doctests.
​2d48ce1	Merge branch 'public/monoids/free_monoids_finitely_generated-20405' into public/misc/names_argument_indexed_generators-17039
​02df281	Fixing doctests.

[git]

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

​1c07d56	Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' of trac.sagemath.org:sage into public/monoids/free_monoids_finitely_generated-20405
​e7914d4	Pulling changes from #17039 to fix doctest with this (#20405) + #20403.
​94f081b	Merge branch 'public/monoids/free_monoids_finitely_generated-20405' into public/misc/names_argument_indexed_generators-17039

[git]

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

​569de0d	Merge branch 'develop' into t/13580/map_reduce
​b07dfe2	Doc of the two implementationsof ActiveTaskCounter
​beebcbc	#13580: Added comment on timing in the doc
​58eca2e	#13580: Removed comment which is now in the doc
​1badd8a	#13580: Renamed ActiveTaskCounter(Posix)
​46cbab9	13580: Fixed doctests to pass on Darwin
​134c1fa	13580: doc rereading
​4c82d1b	Merge branch 'u/hivert/ticket/13580' of trac.sagemath.org:sage into u/hivert/ticket/13580
​67521dd	Merge branch 'u/hivert/ticket/13580' into public/semigroups/iterator_finitely_generated_semigroups-20403
​fc1eb23	Merge branch 'public/misc/names_argument_indexed_generators-17039' of trac.sagemath.org:sage into public/misc/names_argument_indexed_generators-17039

[git]

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

​6272efd	Removing tab character.
​0dfc850	Merge branch 'public/semigroups/iterator_finitely_generated_semigroups-20403' into public/misc/names_argument_indexed_generators-17039

[jdemeyer]

I don't care much about this ticket, just pointing out that it no longer applies.

[git]

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

​5f5bb76

Merge branch 'public/misc/names_argument_indexed_generators-17039' of git://trac.sagemath.org/sage into public/misc/names_argument_indexed_generators-17039

[tscrim]

Green patchbot (essentially).

[jdemeyer]

This is not good:

@@ -127,6 +131,8 @@ def FreeMonoid(index_set=None, names=None, commutative=False, **kwds):
 
     if index_set not in ZZ:
         if names is not None:
+            if isinstance(names, str):
+                names = names.split(',')
             names = normalize_names(len(names), names)
         from sage.monoids.indexed_free_monoid import IndexedFreeMonoid
         return IndexedFreeMonoid(index_set, names=names, **kwds)

This splitting should be handled by normalize_names() (I guess you should replace len(names) by -1).

I also wonder why you do not use normalize_names() in parse_indices_names(). The function normalize_names() is precisely meant to handle names arguments consistently. Don't reinvent the wheel!

[jdemeyer]

Instead of

if 'bracket' not in kwds:
    kwds['bracket'] = False

use ​setdefault

[git]

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

​ad23fbd	Merge branch 'public/misc/names_argument_indexed_generators-17039' of git://trac.sagemath.org/sage into public/misc/names_argument_indexed_generators-17039
​1c1cad1	Use normalize_names.
​627e5e0	Removing code duplication.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​06eae33

Removing code duplication.

[tscrim]

Thank you for looking at this.

comment:18 Good point. IIRC, back when I did this, that was not separated as a standalone function but instead a method of CategoryObject. I also made some other changes to remove code duplication and improve the documentation.

comment:20 I don't want to do that because other keyword options that are used should not default to False, such as scalar_mult.

[git]

Branch pushed to git repo; I updated commit sha1. This was a forced push. New commits:

​76b3be2

Removing code duplication.

[jdemeyer]

Replying to tscrim:

comment:20 I don't want to do that because other keyword options that are used should not default to False, such as scalar_mult.

I don't get your point. I am saying that you can replace

if 'bracket' not in kwds:
    kwds['bracket'] = False

by

kwds.setdefault('bracket', False)

You can do the same for string_quotes but I'm not saying that you must do this for every keyword if you don't want.

[jdemeyer]

Replying to tscrim:

comment:18 Good point. IIRC, back when I did this, that was not separated as a standalone function but instead a method of CategoryObject.

Yes, this was fixed in #19675.

[git]

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

​8f7d3e6

Use setdefault instead of manually checking.

[tscrim]

Replying to jdemeyer:

Replying to tscrim:

comment:20 I don't want to do that because other keyword options that are used should not default to False, such as scalar_mult.

I don't get your point. I am saying that you can replace

if 'bracket' not in kwds:
    kwds['bracket'] = False

by

kwds.setdefault('bracket', False)

You can do the same for string_quotes but I'm not saying that you must do this for every keyword if you don't want.

I misread setdefault. I was thinking it made the dict behave like a defaultdict. I agree that this is a better way to go.

[tscrim]

Patchbot is back to (essentially) green.

[git]

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

​06f1536

Merge branch 'public/misc/names_argument_indexed_generators-17039' of git://trac.sagemath.org/sage into public/misc/names_argument_indexed_generators-17039

[git]

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

​451d60b

Merge branch 'public/misc/names_argument_indexed_generators-17039' of git://trac.sagemath.org/sage into public/misc/names_argument_indexed_generators-17039

[git]

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

​73cf1a7

Updating split_index_keywords.

[tscrim]

Rebased over beta12.

[bsalisbury1]

Changes look good and everything builds and passes on my machine.

[tscrim]

Thank you.