GroebnerWalk.jl is a Julia package providing implementations of Gröbner walk algorithms for computing Gröbner bases over fields on top of Oscar.jl.
GroebnerWalk.jl provides its entire functionality through the function groebner_walk.
The following example demonstrates the usage. First, we define the ideal Oscar.jl.
using Oscar
R, (x,y) = QQ[:x, :y] # define ring ...
I = ideal([y^4+ x^3-x^2+x,x^4]) # ... and idealThen, we can pass the ideal to groebner_walk to calculate the Gröbner basis.
Here, we want a Gröbner basis with respect to the lexicographic ordering on R.
using GroebnerWalk
groebner_walk(I, lex(R)) # compute the Groebner basisThis repository represents the status of the code as a submission for MEGA 2024. It is slated for inclusion into OSCAR as experimental package.
At the moment, the standard walk by Collart, Kalkbrener and Mall (1997) and the generic walk by Fukuda et al. are implemented.
The library is maintained by Kamillo Ferry (kafe (at) kafe (dot) dev) and Francesco Nowell (francesconowell (at) gmail (dot) com).
The current implementation is based on an implementation by Jordi Welp. We thank him for laying the groundwork for this package.
- Collart, S., M. Kalkbrener, and D. Mall. ‘Converting Bases with the Gröbner Walk’. Journal of Symbolic Computation 24, no. 3–4 (September 1997): 465–69. https://doi.org/10.1006/jsco.1996.0145.
- Fukuda, K., A. N. Jensen, N. Lauritzen, and R. Thomas. ‘The Generic Gröbner Walk’. Journal of Symbolic Computation 42, no. 3 (1 March 2007): 298–312. https://doi.org/10.1016/j.jsc.2006.09.004.
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