Change WithRealizations._an_element_ to use a_realization

[tscrim]

As noticed on #21054, there is a discrepancy between one and _an_element_ for parents that are in the category *.WithRealizations, in that the former uses a_realization, whereas the latter uses realizations()[0]. While on #21054, this did uncover an error, this cases problems with the test suite when a realization does not get created before an_element gets called (which I have noticed before).

Thus, I propose to have _an_element_ use a_realization(), which is a required implementation and _an_element_ will also have consistent output no matter which basis is created first.

CC: @nthiery @darijgr

Component: categories

Keywords: days85

Author: Travis Scrimshaw

Branch: f8a1bbb

Reviewer: Florent Hivert

Issue created by migration from https://trac.sagemath.org/ticket/21059

[tscrim]

New commits:

f8a1bbb

Use a_realization() instead of realizations()[0].

[tscrim]

Branch: public/categories/change_an_element_with_realizations-21059

[tscrim]

Commit: f8a1bbb

[AndrewMathas]

comment:2

There are two failing doc-tests in sage/combinat/kazhdan_lusztig when the optional coxeter3 package is installed.

1 item had failures:
   2 of   8 in sage.combinat.kazhdan_lusztig.KazhdanLusztigPolynomial
    [26 tests, 2 failures, 2.76 s]
----------------------------------------------------------------------
sage -t kazhdan_lusztig.py  # 2 doctests failed
----------------------------------------------------------------------

and more failures in sage/libs/coxeter3/.

----------------------------------------------------------------------
sage -t coxeter3/coxeter.pyx  # 256 doctests failed
sage -t coxeter3/coxeter_group.py  # 120 doctests failed
----------------------------------------------------------------------

Not entirely sure what the policy is on doc-tests in optional packages...

[tscrim]

comment:3

Are these are all fixed by #21077?

[hivert]

comment:4

Except for rebasing and doctests this looks good to me. I'll handle the rebasing shortly and put a positive review.

[hivert]

Reviewer: Florent Hivert

[hivert]

Changed keywords from none to days85

[vbraun]

Changed branch from public/categories/change_an_element_with_realizations-21059 to f8a1bbb

[fchapoton]

Changed commit from f8a1bbb to none