sage: M = CombinatorialFreeModule(QQ, DisjointUnionEnumeratedSets([Integers(), Family([])])) sage: M.category() Category of finite dimensional vector spaces with basis over Rational Field sage: M.dimension() +Infinity
And this is the bug that is biting me. CombinatorialFreeModule.__init__ is setting the extra dressing to FiniteDimensional() because of this
sage: NonNegativeIntegers() in Sets().Finite()
False
sage: E = DisjointUnionEnumeratedSets([NonNegativeIntegers(), Family(['x'])]); E
Disjoint union of Family (Non negative integers, Family ('x',))
sage: E in Sets().Finite()
True
sage: E.cardinality()
+Infinity
I suppose this is coming from sage.categories.category_singleton that has the
__contain__ method for Sets().Finite() but the problem is that I am not sure
what is the bug, as a set this is the disjoint union of two sets. So perhaps
the idea behind the above was that this is a finite set with two elements,
one of them being an infinite set. I can live with E in Sets().Finite() being
True (although I don't like it if that was intended)
But I certainly do not like M.category() being finite dimensional. Since basis_keys in CombinatorialFreeModule is Enumerated, I have been using this simple patch to get the right behaviour on the modules and it doesn't seem to break anything.
$ git diff src/sage/combinat/free_module.py
diff --git a/src/sage/combinat/free_module.py b/src/sage/combinat/free_module.py
index 2fbe8b225e..a2bf2a53d6 100644
--- a/src/sage/combinat/free_module.py
+++ b/src/sage/combinat/free_module.py
@@ -449,7 +449,8 @@ class CombinatorialFreeModule(UniqueRepresentation, Module,
IndexedGenerators):
category = ModulesWithBasis(R)
elif isinstance(category, tuple):
category = Category.join(category)
- if basis_keys in Sets().Finite():
+ from sage.rings.infinity import Infinity
+ if basis_keys.cardinality() != Infinity:
category = category.FiniteDimensional()
Parent.__init__(self, base=R, category=category, names=names)
Either way one of the two issues should be corrected I think. Best, R.
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