Hi John,
On 21 Sep., 20:50, john_perry_usm <john.pe...@usm.edu> wrote:
> What about this?
>
> sage: tord = TermOrder(matrix([3,2,4,1,1,0,1,0,0]))
> sage: R.<x,y,z> = PolynomialRing(QQ,'x',3,order=tord)
> sage: (x^2).degree(x)
> 2
> sage: (x^2).degrees()
> (2, 0, 0)
> sage: (x^2).degree()
> 6
>
> Is all of this desirable behavior?
The second part is desirable, IMHO. I believe that the given matrix
order should not impose a degree on the generators. Generator degrees
and matrix order should be independent. But *if* the generators of R
are given the degrees 3,2,4, respectively, then certainly the results
for (x^2).degree(x), (x^2).degrees() and (x^2).degree() are exactly
what I'd like to obtain.
> The docstrings use identical
> language for all three ("maximal degree in ...x", "maximal degree in
> each variable", "maximum degree of any monomial") but have different
> output.
They are not identical. It is "maximal degree of a variable in a
polynomial" versus "maximum degree of all monomials in a polynomial".
I thought it is clear that the "degree of a variable in a monomial" is
the exponent of the variable in the monomial. And the "degree of a
monomial" (not "degree of a *variable in* a monomial") is simply the
degree of the monomial as an element of a graded ring. But I wouldn't
oppose to choose a clearer wording.
Best regards,
Simon
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