Groebner.jl is a Julia package for computing Groebner bases over fields. Groebner.jl is distributed under GNU GPL v2.
For documentation please check outhttps://sumiya11.github.io/Groebner.jl. For a simple example, see below.
You can install Groebner.jl using the Julia package manager. From the Julia REPL, type
importPkg; Pkg.add("Groebner")After the installation, you can run the package tests with
importPkg; Pkg.test("Groebner")The main function provided by Groebner.jl isgroebner.
It works with polynomials from AbstractAlgebra.jl, DynamicPolynomials.jl, and Nemo.jl.
We create a ring of polynomials in 3 variables and a simple polynomial system
usingAbstractAlgebra
R, (x1, x2, x3)=QQ["x1","x2","x3"]
system=[
x1+x2+x3,
x1*x2+x1*x3+x2*x3,
x1*x2*x3-1
]And compute the Groebner basis by passing the system togroebner
usingGroebner
G=groebner(system)#result
3-element Vector{AbstractAlgebra.Generic.MPoly{Rational{BigInt}}}:
x3^3-1
x2^2+x2*x3+x3^2
x1+x2+x3Similarly to AbstractAlgebra.jl, we create a system of polynomials and pass it togroebner
usingDynamicPolynomials, Groebner
@polyvarx1 x2
system=[10*x1*x2^2-11*x1+10,
10*x1^2*x2-11*x2+10]
G=groebner(system)#result
3-element Vector{Polynomial{DynamicPolynomials.Commutative{DynamicPolynomials.CreationOrder}, Graded{LexOrder}, Rational{BigInt}}}:
10//11x2-10//11x1-x2²+x1²
1//1-11//10x2-10//11x2²+10//11x1x2+x2³
1//1-11//10x1+x1x2²This library is maintained by Alexander Demin ([email protected]).
Contributions are very welcome, as are feature requests and suggestions. In particular additional examples and documentation improvements are encouraged. If you encounter any problems, please open an issue or contact a maintainer.
We would like to acknowledge the developers of the msolve library (https://msolve.lip6.fr/), as several components of Groebner.jl were adapted from msolve. In our F4 implementation, we adapt and adjust the code of monomial hashtable, critical pair handling and symbolic preprocessing, and linear algebra from msolve. The source code of msolve is available athttps://github.com/algebraic-solving/msolve.
We thank Vladimir Kuznetsov for helpful discussions and providing the sources of his F4 implementation.
We are grateful to The Max Planck Institute for Informatics and The MAX team at l'X for providing computational resources.
Other software in Julia that can be used for computing Groebner bases:
- AlgebraicSolving.jl
- GroebnerBasis.jl,deprecated, seeOscar.jl
- Singular.jl
If you do not see your package here, we either do not know about it, or forgot to include it, sorry! Feel free to open a PR.
If you find Groebner.jl useful in your work, you can star this repository and citethis paper
@misc{demin2024groebnerjl,
title={Groebner.jl: A package for Gr\ "obner bases computations in Julia},
author={Alexander Demin and Shashi Gowda},
year={2024},
eprint={2304.06935},
archivePrefix={arXiv},
primaryClass={cs.MS}
}