SAGBI and Gr\"obner Bases Detection
Commutative Algebra
2024-04-26 v1 Algebraic Geometry
Abstract
We introduce a detection algorithm for SAGBI basis in polynomial rings, analogous to a Gr\"obner basis detection algorithm previously proposed by Gritzmann and Sturmfels. We also present two accompanying software packages named SagbiGbDetection for Macaulay2 and Julia. Both packages allow the user to find one or more term orders for which a set of input polynomials form either Gr\"obner basis for the ideal they generate or a SAGBI basis for the subalgebra. Additionally, we investigate the computational complexity of homogeneous SAGBI detection and apply our implementation to several novel examples.
Cite
@article{arxiv.2404.16796,
title = {SAGBI and Gr\"obner Bases Detection},
author = {Viktoriia Borovik and Timothy Duff and Elima Shehu},
journal= {arXiv preprint arXiv:2404.16796},
year = {2024}
}