PROJECT DESCRIPTION⌗

The Invariant Calculator was created by Lucas in his senior thesis for college. This “Calculator” allows the exploration of the Derksen-Gandini and Gandini-Ratliff-Rizzolo algorithms for the seeded generation of the minimal subset of monomial invariants, of an invariant ring of polynomials. The code is made available through Github, as linked below. The repository is cleaned, maintained, and updated by Lucas. The calculator is written mostly using Macaulay2, however it uses bash scripts to start the program. This calculator was designed to be run in a Linux command line envoirnment and was developed in Terminal on MacOS. The Invariant Calculator was designed for those that have a base understanding of modern algebra and Invariant Theory.

PROJECT GOALS⌗

The goal of this project was to present the Gandini-Ratliff-Rizzolo algorithm in a manner that is more accessible to those that are interested but have little knowledge of coding and/or computer science. It is a goal that this code, of the Gandini-Ratliff-Rizzolo algorithm will be published with the InvariantRing Package of Macaulay2.

RELEVANT LINKS⌗

• Macaulay2’s offical website: Macualay2: a software system for research in algebraic geometry
• InvariantRing on M2: The InvariantRing package
• The Invariant Calculator on Github: The Invariant Calculator

Research:

• Ideals of Subspace Arrangements (Gandini, 2019)
• The InvariantRing package for Macaulay2 (Ferraro et. al, 2020)
• Finding Minimal Generating Sets of Invariant Polynomials of Diagonalized Finite Abelian Groups (Dolorfino et. al, 2021) (currently unpublished)
• Algorithmic Methods for Computing Monomial Invariants of Abelian Groups (Rizzolo, 2021) (currently unpublished)

Education:

• Ideals, Varieties, and Algorithms (Cox, Little, and O'Shea)
• Invariant Theory (M. Neusel)