Improvements to Sets.WithRealizations

[Nicolas M. Thiéry]

This is a follow up to #7980

Apply:

• trac_12959-improve_with_realizations-fs.patch​
• trac_12959-doctest_fix-fs.patch​
• trac_12959-100_percent_coverage_for_algebras_with_basis-fs.patch​
• trac_12959-remove_lower_from_realization_name-fs.patch​

[Franco Saliola]

Implement default methods for (With)Realizations that use the realization provided by the method a_realization for computations:

• AlgebrasWithBasis.ParentMethods.product is modified to use product_by_coercion if product_on_basis is not available
• Magmas.Realizations added and Magmas.Realizations.ParentMethods.product_by_coercion uses self.a_realization()
• CommutativeAdditiveMonoids.WithRealizations added and CommutativeAdditiveMonoids.WithRealizations.ParentMethods.zero returns self.a_realization().zero()
• Monoids.WithRealizations added and Monoids.WithRealizations.ParentMethods.one returns self.a_realization().one()
• Sets.WithRealizations.ParentMethods.inject_shorthands : injects any shorthands names for realizations provided in the _shorthands attribute
• added _shorthand attribute to the example in sage.categories.example.with_realizations

And update examples/with_realizations.py accordingly.

[Franco Saliola]

100% doctest coverage for algebras_with_basis

[Franco Saliola]

Mike pointed out that algebras_with_basis.py needed only 1 doctest to get 100% coverage, so this latest patch adds one.

[Franco Saliola]

Latest patch switches to using the class name for determining the default realization name (currently, the class name is taken and it is rendered lowercase for some reason; there was a FIXME suggesting this should not be lowercased).

[Jeroen Demeyer]

Please fill in your real name as Reviewer.

[Nicolas M. Thiéry]

For the record: I imported the latest version of the patches in the Sage-Combinat queue, and rebased my functorial construction patch on top of it.

Cheers,

[Nicolas M. Thiéry]

Replying to saliola:

Latest patch switches to using the class name for determining the default realization name (currently, the class name is taken and it is rendered lowercase for some reason; there was a FIXME suggesting this should not be lowercased).

There was a question mark at the end of the FIXME; so this was to be discussed! Oh well, since it's merged in, I guess we can just consider the discussion as closed.