Add Groebner bases of noncommutative polynomials via GBNP

[mathzeta]

The GAP package GBNP, according to its documentation, "provides algorithms for computing Gröbner bases of noncommutative polynomials with coefficients from a field implemented in GAP and with respect to the “total degree first then lexicographical” ordering".

GBNP can be wrapped for Sage by including and adapting this project. The current implementation in Sage for noncommutative Gröbner bases wraps letterplace (from Singular) is restricted to weighted homogeneous elements, and it seem to be somewhat less efficient than GBNP. In any case, it is a good idea to have more than one engine for such tasks.

Note that GAP supports function fields (including with more than one variable), but the libgap interface does not.

CC: @mathzeta @tscrim @trevorkarn

Component: algebra

Keywords: groebner basis

Author: Guy Blachar, Tomer Bauer

Branch/Commit: u/mathzeta2/31446_gbnp_wrapper3 @ 81f11dd

Issue created by migration from https://trac.sagemath.org/ticket/31446

[mkoeppe]

comment:1

Sage development has entered the release candidate phase for 9.3. Setting a new milestone for this ticket based on a cursory review of ticket status, priority, and last modification date.

[trevorkarn]

comment:3

What is the status of this ticket? Looking at the Gitlab repo, it seems like that code might be ready for review. Should that be submitted for review on this ticket?

[mathzeta]

comment:4

Thanks for looking into it, as I did not worked on it for a long time. I just updated the instructions there for GBNP v1.0.4. From a quick skim, it is almost ready:

• The doctests there succeed. There are probably more tests to add from the GBNP docs and from its source code.
• Some functions and methods need proper "Sage-style" documentation. In particular adding # optional: gbnp or gap_gbnp in the doctests.
• An expert in libgap is useful, to check that the code is not doing something completely wrong.
• The growth method, following GBNP, returns either an integer, a list, or a string. I suppose there are better interfaces.

[mathzeta]

Branch: u/mathzeta2/31446_gbnp_wrapper

[mathzeta]

Commit: 9a3773b

[mathzeta]

comment:5

Here is an updated version from that repo, which I think is ready for review.

[mathzeta]

Author: Guy Blachar, Tomer Bauer

[mkoeppe]

comment:7

Stalled in needs_review or needs_info; likely won't make it into Sage 9.5.

[trevorkarn]

comment:8

It seems like there is a merge issue going on - I'm having trouble viewing the diff, and I'm getting the warning

Warning: Merge failed for 9a3773bcd7c0c544d22f3dfd3b74f422543bc2d3

[tscrim]

comment:9

It needs a simple rebase to the latest develop.