In principle it seems okay, but to be honest, I don't think I understand
Sage's polynomial rings. It seems like anything goes:
sage: R.<x> = GF(2)[]
sage: S.<x> = R[]
sage: S
sage: R.0 + S.0
x + x
Why am I allowed to construct S?
With your proposed changes, what happens in the following situation:
sage: T.<x,y> = QQ[]
sage: U.<x,z> = QQ[]
sage: t1, t2 = T.gens()
sage: u1, u2 = U.gens()
Can I now add t1, t2, u1, u2 by automatically creating QQ[x,y,z]?
Do we merge, and therefore identify, QQ[x,y] with QQ[y,x]?
On Saturday, August 26, 2023 at 12:22:39 AM UTC-7 Frédéric Chapoton wrote:
> Dear all,
>
> currently, if x and y are in two different polynomial rings, one cannot
> add them.
>
> I propose in https://github.com/sagemath/sage/pull/36138 a sketch of
> changes that would build a common polynomial ring by taking the union of
> variables. This does not break too many things. Instead many doctests
> checking for coercion failure now report coercion success. There are still
> a few problematic things to solve, in particular about infinite polynomials
> rings.
>
> Please express your opinion about that change of behaviour.
>
> Frederic
>
> Question: what does magma do ?
>
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