Categories for finite (enumerated) sets #12957
Description
There still remains a lot of finite (enumerated) sets that are not in the appropriate categories::
sage: LatticePolytope(matrix(ZZ, [[3,0],[0,3]])).points().category()
Category of objects
See also: #12913
The following examples were originally in the ticket description but are good on sage-6.9.beta1
sage: Permutations().category()
Category of infinite enumerated sets
sage: DirichletGroup(5).category()
Category of finitely generated finite commutative groups
Moreover, with Sage 7.4.beta0 we now have:
sage: CartesianProduct([1,2],[2,3]).category()
... DeprecationWarning: CartesianProduct is deprecated. Use cartesian_product instead
See http://trac.sagemath.org/18411 for details.
#!/usr/bin/env python
Category of Cartesian products of finite enumerated sets
sage: cartesian_product([[1,2],[2,3]]).category()
Category of Cartesian products of finite enumerated sets
sage: Set([1,2,3]).category()
Category of finite sets
Formerly not working, ok in sage 9.3.b6:
sage: Set([1,2,3]).category()
Category of finite sets
sage: (GF(3) ^ 2) in FiniteEnumeratedSets()
True
sage: MatrixSpace(GF(3),2) in FiniteEnumeratedSets()
True
Depends on #12913
CC: @sagetrac-sage-combinat @simon-king-jena @novoselt
Component: categories
Issue created by migration from https://trac.sagemath.org/ticket/12957