Wrap Singular function minbase for homogeneous ideals

[joschmitt]

This introduces minimal_generating_set for homogeneous ideals using Singular's minbase.
Also makes sure that the singular_poly_ring constructed from a MPolyRing_dec is given a weighted monomial ordering corresponding to the grading if the grading is given by positive (or negative) weights.
Resolves #886 as far as I'm concerned.
Note that minbase is also wrapped in Singular.jl, but only for local orderings.

[tthsqe12]

So, I am going to have to do a new Singular.jl release very soon. Any chance you can put this in the correct place (Singular.jl)?

[tthsqe12]

Also, it looks like at least two things are going wrong with singular in the tests.
I will investigate.

[joschmitt]

Also, it looks like at least two things are going wrong with singular in the tests. I will investigate.

It's probably my fault, but I haven't looked into it yet.

[joschmitt]

So, I am going to have to do a new Singular.jl release very soon. Any chance you can put this in the correct place (Singular.jl)?

Okay, sure.

[joschmitt]

So, I am going to have to do a new Singular.jl release very soon. Any chance you can put this in the correct place (Singular.jl)?

It would be good, if one could check whether an ideal is homogeneous in Singular.jl for this, but I couldn't find a function for that. In Singular there is homog; how do I use this in Singular.jl?

[joschmitt]

Also, it looks like at least two things are going wrong with singular in the tests. I will investigate.

It's probably my fault, but I haven't looked into it yet.

So yeah, it was my fault (and not Singular's).

[tthsqe12]

So, I am going to have to do a new Singular.jl release very soon. Any chance you can put this in the correct place (Singular.jl)?

It would be good, if one could check whether an ideal is homogeneous in Singular.jl for this, but I couldn't find a function for that. In Singular there is homog; how do I use this in Singular.jl?

There is no equivalent of homog in Singular.jl yet because the corresponding code is missing from libsingular_julia.jll. It would would have to be written, and then we can use it in the next version of libsingular_julia.jll.
oscar-system/libsingular-julia#54

[wdecker]

@joschmitt

In Singular, there is also the more general isHomogeneous from multigrading.lib

[joschmitt]

Then I don't see what I can do on the Singular.jl side. One only needs to extend the check in line https://github.com/oscar-system/Singular.jl/blob/e2d8e79e44af39119559181a0437970f3b062f8f/src/ideal/ideal.jl#L915 to also allow homogeneous ideals when homog is available.
(In principle, idMinBase allows all kind of ideals, but will print
// minbase applies only to the local or homogeneous case over coefficient fields
if it doesn't like the input.)

[tthsqe12]

Alright. Just keep it here, and I'll open an issue for moving it eventually.

[hannes14]

Am Mon, Mar 21, 2022 at 11:39:45PM -0700 schrieb Wolfram Decker:

In Singular, there is also the more general isHomogeneous from multigrading.lib

But multigrading.lib uses Singulars attributes which we do not have in libsingular-julia/Singular.jl/Oscar