Tensor products of commutative algebras do not know they are commutative rings

[tscrim]

sage: X = algebras.Shuffle(QQ, 'ab')
sage: Y = algebras.Shuffle(QQ, 'bc')
sage: X in CommutativeRings()
True
sage: Y in CommutativeRings()
True
sage: T = tensor([X,Y])
sage: T in CommutativeRings()
False

CC: @mkoeppe @jhpalmieri @fchapoton @mantepse

Component: categories

Author: Travis Scrimshaw

Branch/Commit: 5776c61

Reviewer: Frédéric Chapoton

Issue created by migration from https://trac.sagemath.org/ticket/34453

[tscrim]

Commit: 5776c61

[tscrim]

Branch: public/categories/tensor_commutative_rings-34453

[tscrim]

New commits:

5776c61

Adding the category of commutative rings to the category of tensor products of commutative algebras.

[fchapoton]

comment:3

would this work too for the tensor product of a shuffle algebra A and a polynomial ring B ? maybe add this kind of simple example ?

I tried A.tensor(B) on vanilla sage and it failed.

[tscrim]

comment:4

Sadly, a polynomial ring does not (yet) know it is an algebra over its base ring.

[fchapoton]

comment:5

the patchbot reports a strange doctest failure, most probably unrelated

if you agree with this diagnostic, you can set to positive

[fchapoton]

Reviewer: Frédéric Chapoton

[tscrim]

comment:6

I saw that on another ticket, so it is definitely unrelated.

Thank you.

[mantepse]

comment:7

Replying to Travis Scrimshaw:

Sadly, a polynomial ring does not (yet) know it is an algebra over its base ring.

Could you give an example for this?

sage: P.<x,y> = Integers(8)[]
sage: P in Algebras(P.base_ring())
True

[tscrim]

comment:8

I must be misremembering then.

[vbraun]

Changed branch from public/categories/tensor_commutative_rings-34453 to 5776c61