On Nov 29, 9:07 am, Simon King <simon.k...@uni-jena.de> wrote:
> > 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.
agreed.
> > "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.
>
Oh, I was thinking that there is a polynomial subring of QQ['a','b']
generated by 'a', and that according to the uniqueness/immutability
idea, this subring ought to be THE (dense) polynomial ring in 'a' over
QQ. This contradicts the description of the current (undesirable)
containment for multivariate polynomial rings (as John mentioned).
That docstring reads:
"""
This definition of containment does not involve a natural
inclusion from rings with less variables into rings with more.
"""
Since the ticket will be reversing this behavior, I thought it should
have some justification.
-Niles
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