Hi John!

On Sep 5, 3:05 pm, john_perry_usm <john.pe...@usm.edu> wrote:
> > What do people think?
> >  * Should it (in addition to the current behaviour) be possible to
> > define a matrix ordering by a matrix and a block ordering by a list or
> > tuple?
>
> Although you are in favor of the other two solutions, I think that
> this solution is quite natural, inasmuch as it's what I'd want to do
> intuitively. IIRC, Maple does this as well.

Martin Albrecht pointed out in a related thread
http://groups.google.com/group/sage-devel/browse_thread/thread/497bfc40ea5f17b8
that one can also work with TermOrder objects, which allow for an easy
creation of block orderings.

TermOrder does not support proper matrix orderings yet, but I think
this would be the natural place to implement it (hence, not in the
PolynomialRing constructor).

Example:
  sage: M = Matrix(2,2, [1,3,1,0])
  sage: R.<a,b,c,d,e,f> = PolynomialRing(QQ, order=TermOrder(M)
+TermOrder('deglex',3))

Do you think that this would be an appropriate / natural /
convenient / intuitive way to create a block ordering involving a
matrix ordering?

I think it would be easy to make conversion of R into a Singular ring
work (just a few lines in TermOrder.__init__, I guess). However,
implementing it such that it genuinely works in Sage seems to require
substantial work on libsingular.

Cheers
Simon

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