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SAGBI and Gr\"obner Bases Detection

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arxiv 2404.16796 v1 pith:YG7JGLIZ submitted 2024-04-25 math.AC math.AG

Viktoriia Borovik , Timothy Duff , Elima Shehu This is my paper · ORCID
classification math.ACmath.AG
keywords basisdetectionsagbiobneralgorithmpackagesaccompanyingadditionally
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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.

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  1. The SagbiHomotopy.jl package for solving polynomial systems

    math.AG 2025-06 conditional novelty 5.0 of 10

    SagbiHomotopy.jl implements SAGBI-basis homotopy continuation, reducing path counts for horizontally parameterized polynomial systems compared with polyhedral homotopies.

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