Meta-ticket: Deprecate CombinatorialClass in favor of the EnumeratedSet's categories

[nthiery]

All classes that currently inherit from CombinatorialClass should instead inherit from Parent and register themselves in one of the categories (*EnumeratedSets, *FiniteEnumeratedSets, or *InfiniteEnumeratedSets). For examples, see e.g. FiniteEnumeratedSets().example().

• Expected benefits:
  • Uniform interface
  • Support for TestSuite
  • Support for conversions, coercions, and morphisms, in particular for bijections (as morphisms in the category of Sets with bijection, with properly defined domain and co-domain rather than python functions).
• Steps:
  1. Let CombinatorialClass inherits from Parent (mostly done Have CombinatorialClass inherits from Parent #8910)
  2. For each CombinatorialClass C:
  • Have C inherit directly from Parent
  • Ensure that C.__init__ sets up the proper category (Finite|Infinite)...
  • Add TestSuite(C).run() to the doctests and make all the tests pass
  • Have a properly setup attribute C.Element and use C.element_class (as defined by the categories) when constructing elements
  • Ensure proper unique representation behavior by having C inherit both from UniqueRepresentation and Parent
  3. Deprecate and remove CombinatorialClass
  4. Turn all the factory functions into factory classes by mean of ClasscallMetaClass; see PerfectMatching and Trees for an advanced example.

See also: http://wiki.sagemath.org/CombinatorialClass

CC: @sagetrac-sage-combinat

Component: combinatorics

Issue created by migration from https://trac.sagemath.org/ticket/12913

[nthiery]

Description changed:

--- 
+++ 
@@ -16,3 +16,4 @@
   3. Deprecate and remove `CombinatorialClass`
   4. Turn all the factory functions into factory classes by mean of `ClasscallMetaClass`; see `PerfectMatching` and `Trees` for an advanced example.
 
+See also: http://wiki.sagemath.org/CombinatorialClass

[tscrim]

comment:2

Part of the work is done in #13605 (partition.py) and #14063 (compositions). More to come.

[tscrim]

comment:3

More work:

• Set partitions in Reorganization of set partitions #14140,
• skew* in Remove CombinatorialClass from skew* #14101.

[tscrim]

comment:4

Permutations in #14772.

[tscrim]

comment:5

Integer vectors in #12453.