Make L.<x> syntax work for LazyLaurentSeriesRing

[slelievre]

Following #27347, one can use

sage: from sage.rings.lazy_laurent_series_ring import LazyLaurentSeriesRing
sage: L = LazyLaurentSeriesRing(ZZ, 'z')
sage: x = L.gen()

It would be nice to have the syntactic sugar

sage: L.<x> = LazyLaurentSeriesRing(ZZ)

work, just as it does for non-lazy:

sage: L.<x> = LaurentSeriesRing(ZZ)

The Sage preparser actually transforms the L.<x> input as follows:

sage: preparse('L.<x> = LazyLaurentSeriesRing(ZZ)')
"L = LazyLaurentSeriesRing(ZZ, names=('x',)); (x,) = L._first_ngens(1)"

so methods gens and _first_ngens are needed for LazyLaurentSeriesRing.

[klee]

Does your proposal include importing LazyLaurentSeriesRing at startup time?

[slelievre]

It is the case for LazyPowerSeriesRing, so that would be consistent.

[klee]

Replying to slelievre:

It is the case for LazyPowerSeriesRing, so that would be consistent.

I fear that it increases startup time. Perhaps using lazy_import is necessary.

[slelievre]

Maybe that is the case for LazyPowerSeriesRing too? I don't know how to check that...

[jhpalmieri]

Doesn't look like it's lazily imported, see the third hit in the search:

sage: search_src('import', 'LazyPowerSeriesRing')
categories/highest_weight_crystals.py:378:                from sage.combinat.species.series import LazyPowerSeriesRing
categories/sets_with_grading.py:217:            from sage.combinat.species.series import LazyPowerSeriesRing
combinat/species/all.py:6:from .series import LazyPowerSeriesRing
combinat/species/generating_series.py:81:from .series import LazyPowerSeriesRing, LazyPowerSeries
combinat/species/series.py:51:            sage: from sage.combinat.species.series import LazyPowerSeriesRing

[klee]

New commits:

​bdfc88b

Make L.<z> work

[klee]

It's not lazily imported yet. Let's see how this affects the startup time first.

[tscrim]

I would just lazily import it. There is no real harm in doing that. It just might take a moment to load when first using it in Sage. It is quite difficult to see how a single import changes startup time (unless it is really big); it is a "death by a 1000 needles" thing where it is the culmination of all the different modules.

[git]

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

​084c44f

Change x to z

[git]

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

​3f28452

Switch to lazy_import

[tscrim]

Ready for review?

[tscrim]

LGTM.