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SubalgebraBases in Macaulay2

Michael Burr, Oliver Clarke, Timothy Duff, Jackson Leaman, Nathan Nichols and Elise Walker

Vol. 14 (2024), 97–109
DOI: 10.2140/jsag.2024.14.97

We describe a recently revived version of the software package SubalgebraBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subalgebra bases — which are also known as SAGBI bases, or canonical bases, and form a special class of Khovanskii bases — for polynomial rings and their quotients. We provide an overview of the design and functionality of the SubalgebraBases package and demonstrate how the package works on several motivating examples.

SAGBI basis, Newton–Okounkov body, computer algebra, Macaulay2, symbolic computation
Mathematical Subject Classification
Primary: 14-04, 68W30
Supplementary material

A package for finding canonical subalgebra bases (SAGBI bases).

Received: 23 February 2023
Revised: 12 March 2024
Accepted: 18 March 2024
Published: 31 May 2024
Michael Burr
Clemson University
Clemson, SC
United States
Oliver Clarke
University of Edinburgh
United Kingdom
Timothy Duff
Department of Mathematics
University of Washington
Seattle, WA
United States
Jackson Leaman
Clemson University
Clemson, SC
United States
Nathan Nichols
Department of Mathematics and Statistical Sciences
Marquette University
Milwaukee, WI
United States
Elise Walker
Center for Computing Research
Sandia National Laboratories
Albuquerque, NM
United States