Simon,

You're right, and you pointed the way to an easy solution.  Thanks for
the help.

Jeff


On Jun 5, 11:46 pm, Simon King <simon.k...@uni-jena.de> wrote:
> Hi Jeff,
>
> On 6 Jun., 04:33, Jeff Stroomer <jstroom...@hotmail.com> wrote:
>
> >     M = Matrix([
> >       [ 1,  0,  0,  0],
> >       [ 0,  1,  1,  1],
> >       [ 0,  0,  1,  0],
> >       [ 0,  0,  0,  1],
> >     ])
> >     Rt = PolynomialRing(GF(101), order = TermOrder(M), names = 'e, t,
> > x, y')
> >     print Rt(g).degree()
>
> > The first print reports that the degree of g is 7, which is correct,
> > but the second reports the degree is 0.
>
> Both answers are correct. In a matrix order, the first row (resp. the
> first column, AFAIK both conventions appear in the literature) of the
> matrix provides the degrees of the generators. Here, we have
>
> sage: Rt.<e,t,x,y> = PolynomialRing(GF(101), order = TermOrder(M))
> sage: e.degree()
> 1
> sage: t.degree()
> 0
> sage: x.degree()
> 0
> sage: y.degree()
> 0
>
> Hence, IN THAT RING, x^5-x*y^6 is indeed of degree zero. In the other
> ring, it is of degree 7.
>
> Cheers,
> Simon

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