minimal_generating_set for homogeneous ideals

[hannes14]

minimal_generating_set should be extended to
homogeneous/weighted homogeneous ideals
(also: need a test for that)

[tthsqe12]

Can we have an example? and a way to test if the homogeneous input is valid in idMinBase?

[wdecker]

What precisely is minimal_generating_set meant to do in the non-homogeneous case?

[hannes14]

returns a minimal set of generators of an ideal, resp. module, if the input is either homogeneous or if the ordering is local.
from the singular manual:
ring r=181,(x,y,z),(c,ls);
ideal id2=x2+xyz,y2-z3y,z3+y5xz;
ideal id4=maxideal(3)+id2;
minbase(id4);
==> _[1]=x2
==> _[2]=xyz+x2
==> _[3]=xz2
==> _[4]=y2
==> _[5]=yz2
==> _[6]=z3

[wdecker]

Thx @hannes14 So the task here ist to extend something from the local to the graded case?

[hannes14]

Singular.jl has minimal_generating_set for the local case,
it should be extended to the homogeneous ideals

[wdecker]

O.k. , then the question is should that be as general as possible, that is, should this apply to all (multi)gradings for which we have Nakayama's lemma?

[tthsqe12]

"homogeneous ideals" what is the definition of this, and how do I check it?

[wdecker]

@tthsqe12 I sent you an email ansering your questions