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

[Nicolas M. Thiéry]

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 #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

[Travis Scrimshaw]

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

[Travis Scrimshaw]

More work:

• Set partitions in #14140,
• skew* in #14101.

[Travis Scrimshaw]

Permutations in #14772.

[Travis Scrimshaw]

Integer vectors in #12453.

[Frédéric Chapoton]

Status

git grep -c "import.*CombinatorialClass"
src/sage/categories/enumerated_sets.py:1
src/sage/combinat/all.py:1
src/sage/combinat/cartesian_product.py:1
src/sage/combinat/combination.py:1
src/sage/combinat/finite_class.py:1
src/sage/combinat/graph_path.py:1
src/sage/combinat/multichoose_nk.py:1
src/sage/combinat/necklace.py:1
src/sage/combinat/non_decreasing_parking_function.py:1
src/sage/combinat/parking_functions.py:1
src/sage/combinat/partition.py:1
src/sage/combinat/restricted_growth.py:1
src/sage/combinat/root_system/root_lattice_realizations.py:1
src/sage/combinat/sf/ns_macdonald.py:1
src/sage/combinat/species/structure.py:1
src/sage/combinat/symmetric_group_representations.py:1
src/sage/combinat/tuple.py:1
src/sage/combinat/words/shuffle_product.py:1
src/sage/dynamics/flat_surfaces/strata.py:2
src/sage/graphs/linearextensions.py:1
src/sage/sets/family.py:1

[Travis Scrimshaw]

That's actually slightly worse than I thought, but it is good progress. I suspect most of them should be easy changes. From a quick look:

src/sage/combinat/root_system/root_lattice_realizations.py

is easy to fix as per the comment there (which really moves the issue to the EnumeratedSets category).

However

src/sage/combinat/symmetric_group_representations.py

is harder as the CombinatorialClass is behaving something between a category and a parent. At least its elements are morphisms from the SGA to a matrix space, but not with the same codomain. Also, I think of a representation as a vector space with an action together. Well, representation theory in Sage is sorely lacking currently and is something I've only been able to work on in a limited capacity so far.

[Frédéric Chapoton]

see #23422

[Frédéric Chapoton]

see #24485 for necklaces

and #24486 for "restricted growth arrays"

[Frédéric Chapoton]

#26384 for non-decreasing parking functions

[Frédéric Chapoton]

• #20764 for parking functions

• #25864 for linear extensions (deprecation before removal)

• #28825 for combinat/tuple

[Frédéric Chapoton]

remains now

• sage/categories/enumerated_sets.py:1
• sage/combinat/combination.py:1
• sage/combinat/graph_path.py:1
• sage/combinat/parking_functions.py:1
• sage/combinat/shuffle.py:1
• sage/combinat/species/structure.py:1
• sage/combinat/symmetric_group_representations.py:1
• sage/combinat/words/shuffle_product.py:1
• sage/sets/family.py:1 (easy removal, but must be done at the end)

[Frédéric Chapoton]

• #30904 for sage/combinat/words/shuffle_product.py

• #30907 for Parking functions

• #30908 for combination.py

• #30962 for shuffle

• #30963 for graph_path

• #31079 for symmetric_group_representations.py

[Martin Rubey]

@chapoton: concerning the species problem, would you be interested in participating in an online species workshop in February - both as mathematician and as sagemath aficionado?

[Frédéric Chapoton]

Oh, there seems to remains more with sub-classes (including MapCombinatorialClass) in

src/sage/categories/enumerated_sets.py
src/sage/combinat/combinat.py

[Frédéric Chapoton]

deprecating the unused variants in #31545

[Matthias Köppe]

I have opened #32121 for MapCombinatorialClass.

[Matthias Köppe]

#33384: Deprecate global imports of CombinatorialObject, CombinatorialClass, MapCombinatorialClass