SAGBI and Gr\"obner Bases Detection
Viktoriia Borovik, Timothy Duff, Elima Shehu
TL;DR
This paper presents a new algorithm for detecting SAGBI bases in polynomial rings, along with software tools for identifying term orders that produce Gr"obner or SAGBI bases, and explores the complexity of this detection.
Contribution
It introduces a SAGBI detection algorithm, provides software implementations, and analyzes the computational complexity involved.
Findings
Successful implementation of SAGBI detection in Macaulay2 and Julia
Identification of term orders for which polynomials form SAGBI or Gr"obner bases
Analysis of the computational complexity of SAGBI detection
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.
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Taxonomy
TopicsMedical Imaging Techniques and Applications · Analytical Chemistry and Chromatography · Mass Spectrometry Techniques and Applications