Improvements to Sets.WithRealizations

[nthiery]

This is a follow up to #7980

Apply:

• attachment: trac_12959-improve_with_realizations-fs.patch
• attachment: trac_12959-doctest_fix-fs.patch
• attachment: trac_12959-100_percent_coverage_for_algebras_with_basis-fs.patch
• attachment: trac_12959-remove_lower_from_realization_name-fs.patch

Depends on #12953

CC: @sagetrac-sage-combinat @sagetrac-chrisjamesberg @zabrocki

Component: categories

Keywords: realizations, sd40

Author: Nicolas M. Thiéry, Franco Saliola

Reviewer: Mike Zabrocki

Merged: sage-5.3.beta0

Issue created by migration from https://trac.sagemath.org/ticket/12959

[saliola]

Attachment: trac_12959-improve_with_realizations-fs.patch.gz

[saliola]

Changed keywords from realizations to realizations, sd40

[saliola]

Changed author from Nicolas M. Thiéry, ... to Nicolas M. Thiéry, Franco Saliola

[saliola]

comment:1

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.

[saliola]

Attachment: trac_12959-doctest_fix-fs.patch.gz

[saliola]

Attachment: trac_12959-100_percent_coverage_for_algebras_with_basis-fs.patch.gz

100% doctest coverage for algebras_with_basis

[saliola]

comment:3

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

[saliola]

comment:4

Attachment: trac_12959-remove_lower_from_realization_name-fs.patch.gz

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).