Hi Niles,
On 29 Nov., 14:22, Niles <[email protected]> wrote:
> Thanks for the pointers. If I'm understanding correctly, everyone is
> in favor of using the default containment inherited from Parent;
I, for one, am.
> so
> that we would have
>
> sage: 3 in PolynomialRing(QQ,'a,b')
> True
>
> sage: PolynomialRing(QQ,'a').gen() in PolynomialRing(QQ,'a,b')
> True
Yes. But note that there must be a pushout of the parents:
sage: QQ['c','a']('a')==ZZ['b','a','d']('a')
is false, will be false, and should be false.
> The proposed behavior would be consistent with the uniqueness and
> immutability of polynomial rings:
>
> http://www.sagemath.org/doc/reference/sage/rings/polynomial/polynomia...
>
> "UNIQUENESS and IMMUTABILITY: In Sage there is exactly one single-
> variate polynomial ring over each base ring in each choice of
> variable, sparseness, and implementation. There is also exactly one
> multivariate polynomial ring over each base ring for each choice of
> names of variables and term order. ..."
I don't see how these two details are related, but anyway, I am +1 for
having standard containment tests for multivariate polynomial rings.
Cheer,
Simon
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