Make parent/element classes independent of base rings

[simon-king-jena]

At #11900 and sage-combinat-devel, as well as in some comments in sage/categories/category.py, the idea was discussed to make, for example, Algebras(GF(3)).parent_class==Algebras(GF(5)).parent_class - hence, make the parent/element classes as independent from the base of a category as possible.

This is implemented in this patch by introducing an abstract class CategoryWithParameters which uses pickling by "weak construction" for its element and parent classes. Now:

• For a join category, the parent/element class depend only on the parent/element class of its super categories.
• For a Category_over_base (e.g. Modules, Algebras, Schemes, ...), the parent/element class depend only on the category of the base.
• For a bimodule, the parent/element class depend only on the category of the left and right bases.

In the process, this patch also:

• Adds a method Category._make_named_class providing a unified way to create parent and element classes (and later on morphism classes)
• Extends the interface of dynamic_class to customize caching and pickling
• Rename the experimental class IdempotentSemigroups.ElementMethods and remove its super class, and discards unused code there.

Apply

• attachment: trac11935_weak_pickling_by_construction-nt.patch
• attachment: trac_11935-weak_pickling_by_construction-review-ts.patch

Depends on #9138 Depends on #11900 Depends on #11943 Depends on #12875 Depends on #12876 Depends on #12877

CC: @jdemeyer @sagetrac-sage-combinat

Component: categories

Keywords: parent class, element class

Author: Simon King

Reviewer: Nicolas M. Thiéry, Travis Scrimshaw

Merged: sage-5.11.beta1

Issue created by migration from https://trac.sagemath.org/ticket/11935

[jdemeyer]

Changed reviewer from Nicolas Thiery, Travis Scrimshaw to Nicolas M. Thiéry, Travis Scrimshaw