Vol. 11, No. 1, 2021

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Threaded Gröbner bases: a Macaulay2 package

Sonja Petrović and Shahrzad Zelenberg

Vol. 11 (2021), 123–127
Abstract

The complexity of Gröbner computations has inspired many improvements to Buchberger’s algorithm over the years. Looking for further insights into the algorithm’s performance, we offer a threaded implementation of the classical Buchberger algorithm in Macaulay2. The output of the main function of the package includes information about lineages of nonzero remainders that are added to the basis during the computation. This information can be used for further algorithm improvements and optimization.

Keywords
Gröbner basis, distributed computation, lineages, S-pairs
Mathematical Subject Classification
Primary: 13P10
Supplementary material

Computing a Groebner basis using the classical Buchberger with multiple threads

Milestones
Received: 19 July 2020
Revised: 6 August 2021
Accepted: 8 October 2021
Published: 20 February 2022
Authors
Sonja Petrović
Department of Applied Mathematics
Illinois Institute of Technology
Chicago, IL
United States
Shahrzad Zelenberg
Lake Forest College
Department of Mathematics and Computer Science
Lake Forest, IL
United States