This is now Trac 10355:
http://trac.sagemath.org/sage_trac/ticket/10355
I've uploaded a patch which simply deletes the definition of
__contains__ for multivariate polynomials, thus falling back to the
definition from Parent. Unfortunately, this causes some doctest
failures in schemes/generic/toric_variety.py and misc/trace.py. I'll
have to look into those later (unless someone else wants to jump
in!). In any case, I guess we should take any further discussion to
that ticket.
best,
Niles
On Nov 29, 12:54 pm, Niles <nil...@gmail.com> wrote:
> 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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