support for weighted term orders in normal_basis

[mwageringel]

As a follow-up to #29543, this ticket changes the normal_basis method of ideals to handle the case of weighted term orders.

With this change, the degree of the monomials in the normal basis is taken with respect to the weighted degree (which agrees with Sage's notion of degree).

sage: R.<x,y,z> = PolynomialRing(QQ, order=TermOrder('wdegrevlex', (1, 2, 3)))
sage: I = R.ideal(x*y^2 + x^5, z*y + x^3*y)
sage: I.normal_basis(degree=9)
[x^2*y^2*z, x^3*z^2, x*y*z^2, z^3]
sage: all(f.degree() == 9 for f in _)
True

This also came up in an Ask SageMath question.

The implementation uses the Singular function weightKB.

CC: @kwankyu @tscrim @heluani

Component: commutative algebra

Keywords: singular

Author: Markus Wageringel

Branch/Commit: f0604bd

Reviewer: Travis Scrimshaw

Issue created by migration from https://trac.sagemath.org/ticket/29625

[mwageringel]

Author: Markus Wageringel

[mwageringel]

Commit: f0604bd

[mwageringel]

Branch: u/gh-mwageringel/29625

[mwageringel]

New commits:

f0604bd

29625: support weighted term orders in normal_basis

[tscrim]

Reviewer: Travis Scrimshaw

[tscrim]

comment:2

LGTM.

[vbraun]

Changed branch from u/gh-mwageringel/29625 to f0604bd