I would recommend looking at how Mathematica handles this sort of
thing. One of the things I miss is its ability to selectively treat
different variables as either part of a coefficient ring or as
multivariate polynomials. For example:
GroebnerBasis[{x^2*y - y, Sin[z]*x*y^2 - y*Sin[z]}, {x, y}]
{-y Sin[z] + y^3 Sin[z], x y Sin[z] - y^2 Sin[z], -y + x^2 y}
GroebnerBasis[{x^2*y - y, Sin[z]*x*y^2 - y*Sin[z]}, {y}]
{-y + x^2 y, -x y Sin[z] + y^2 Sin[z]}
Some sort of similar syntax might be required with our symbolic ring.
-Marshall
On Jul 21, 1:56 pm, William Stein <wst...@gmail.com> wrote:
> On Tue, Jul 21, 2009 at 9:44 AM, William Stein<wst...@gmail.com> wrote:
> > On Tue, Jul 21, 2009 at 9:37 AM, Ryan Hinton<iob...@email.com> wrote:
>
> >> Are Groebner bases for multivariate polynomials over the symbolic ring
> >> supposed to work?
>
> > No, they are definitely not supposed to work.
>
> I take that back. The toy implementation should work over anything
> that behaves like a field. I guess SR is supposed to model a field,
> maybe, sort of...
>
> William
>
>
>
> > William
>
> >> Here's what I get in Sage 4.0.1.rc2:
>
> >> sage: R2.<a,b> = SR[]
> >> sage: I2 = [a*b+a, a*a] * R2
> >> sage: G2 = I2.groebner_basis()
> >> verbose 0 (2247: multi_polynomial_ideal.py, groebner_basis) Warning:
> >> falling back to very slow toy implementation.
> >> ---------------------------------------------------------------------------
> >> AttributeError Traceback (most recent call
> >> last)
> >> ...
> >> AttributeError: 'MPolynomialRing_polydict' object has no attribute
> >> 'monomial_divides'
> >> sage:
>
> >> I probably don't have the understanding (or time) to fix this, but I
> >> wanted to make sure I'm not doing something wrong.
>
> >> Thanks!
>
> >> - Ryan
>
> > --
> > William Stein
> > Associate Professor of Mathematics
> > University of Washington
> >http://wstein.org
>
> --
> William Stein
> Associate Professor of Mathematics
> University of Washingtonhttp://wstein.org
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