GroebnerWalk.jl

GroebnerWalk.jl provides several variants of Gröbner walk algorithms for converting Gröbner bases. For this, we make use of the computer algebra system OSCAR.

Installation

For this package we require Julia version 1.10 or higher and OSCAR in at least version 1.0.

Both OSCAR and this package can be installed using the Julia package manager. Open the Julia prompt and type ] and enter the following command

pkg> add Oscar, GroebnerWalk

Equivalently, you can enter

julia> using Pkg; Pkg.add(["Oscar", "GroebnerWalk"])

Quick start

The Gröbner walk is also implemented in OSCAR and can be used by calling the function groebner_walk. Thus, it is sufficient to load OSCAR to use the Gröbner walk.

using Oscar

R, (x,y) = QQ[:x, :y]            # define ring ...
I = ideal([y^4+ x^3-x^2+x,x^4])  # ... and ideal

groebner_walk(I)                 # compute the Groebner basis

If you specifically wish to use the implementation contained in this package, you need to call it using the fully qualified name GroebnerWalk.groebner_walk.