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The InvariantRing package for Macaulay2

Luigi Ferraro, Federico Galetto, Francesca Gandini, Hang Huang, Matthew Mastroeni and Xianglong Ni

Vol. 14 (2024), 5–11

We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of finite groups, the updated package adds functionality for computing invariants of diagonal actions of tori and finite abelian groups, as well as invariants of arbitrary linearly reductive group actions. The implementation of the package has been completely overhauled with the aim of serving as a unified resource for invariant theory computations in Macaulay2.

Macaulay2, invariants, group actions
Mathematical Subject Classification
Primary: 13-04, 13A50, 13P25
Supplementary material

InvariantRing is a package implementing algorithms to compute invariants of linearly reductive groups.

Received: 16 December 2020
Revised: 26 July 2022
Accepted: 14 September 2023
Published: 26 March 2024
Luigi Ferraro
School of Mathematical and Statistical Sciences
University of Texas Rio Grande Valley
Edinburg, TX
United States
Federico Galetto
Department of Mathematics and Statistics
Cleveland State University
Cleveland, OH
United States
Francesca Gandini
Department of Mathematics, Statistics, and Computer Science
St. Olaf College
Northfield, MN
United States
Hang Huang
Department of Mathematics
Texas A&M University
College Station, TX
United States
Matthew Mastroeni
Iowa State University
Ames, IA
United States
Xianglong Ni
Department of Mathematics
University of California Berkeley
Berkeley, CA
United States