Hi John,

On 22 Sep., 23:46, john_perry_usm <john.pe...@usm.edu> wrote:
> Are you saying the first row of a matrix term ordering determines the
> degree of the generators?

I said two things.

One statement was: The matrix term ordering should not interfere with
the degrees of the generators. It must be possible to define
generators in degree 2,3,4 and order the monomials with a matrix order
given by a matrix that does not contain any of the number 2,3,4.

Sadly, Singular does not offer that flexibility (yet?). And since
multivariate polynomial rings in Sage largely depend on Singular, it
might be difficult to work around in Sage.

However, the other statement was: *If* one has defined a polynomial
ring with generators x,y,z in degrees 2,3,4, then (x*y*z).degree()
should return 9; returning 3 would be a bug. (x*y*z).degrees() should
return (1,1,1).

Hence, *if* one can not fix the first problem (Singular taking the
generator degrees from the order matrix) then it would mean to
deliberately create a bug if we would override p.degree() by, say,
sum(p.degrees()) (for p=x*y*z in my example above, it would return 3).

I'd rather have one bug than two.

By the way: Next week, there will be Sage Days in Kaiserslautern, the
home of Singular. Perhaps one could try to convince Singular people to
break the link between the first row of an order matrix and the degree
vector.

Cheers,
Simon

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