Hi Simon,
Thanks for your feedback,
On Wed, Feb 10, 2010 at 04:51:37AM -0800, Simon King wrote:
> > > sage: p = 3*x^2+2*x+1
> > > sage: p.leading_coefficient()
> > > 3
> >
> > Florent is also +1 on this convention, and I just fixed the patch
> > accordingly. But it is still time to rollback. Please vote!
>
> What is x in the above expression? Is it var('x')?
Oh right, I forgot the:
sage: P.<x> = QQ[]
beforehand.
> Generally, since I work with Groebner basis, I am of course all for
> keeping in mind that polynomial rings come with a monomial order, that
> these orders may be different, that the leading monomial/term/
> coefficient depends on this order, and that rings with the same base
> ring and variable names are different if their monomial orders differ.
Definitely.
Here the general context is that of a free modules (or algebras/...),
whose basis is indexed by some set, which includes multivariate
polynomials. The core of the question is whether we have an agreement
that the ``leading term`` should be that with "largest" index,
whatever largest means given the term order specified by the parent (a
typical example would be the largest partition lexicographically for
symmetric functions).
Best,
Nicolas
--
Nicolas M. Thiéry "Isil" <[email protected]>
http://Nicolas.Thiery.name/
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