Macaulay2 with students

Macaulay2, also known as M2, is a computer algebra software designed for research in algebraic geometry and commutative algebra. Using M2, learners of mathematics are able to experiment with examples and gain intuition to form conjectures. Its built-in algebraic objects make it especially convenient for fast computations involving Groebner bases. The development is community-based, the code is open source, and the functionalities are continuously improving!

Given the sophistication of the software, installation requires terminal use and some package management. In an effort to onboard undergraduates quickly to Macaulay2, Francesca has been involved in the GitHub for Mathematicians or g4m project, first as a trainee, and then a trainer of others. Her training and efforts with students are informed by the principles of COCOA.

In Spring 2025, a first team of students, Inti and Sam, learned and documented workflows that require minimal specialized coding knowledge. The end result was a contribution to g4m, Chapter 10: Macaulay2. The documentation focuses on how to set up and run Macaulay2 on a Codespace as this allows for students to edit M2 code and contribute without having to install it on their local machine. Once they were hooked on M2, they were motivated to acquire the computing skills required to successfully install it on their local machines!

In Summer 2025, Sam trained Sasha, Gordie, and Marcus with these materials to jump start their work with Macaulay2, while learning the invariant theory necessary to conceptualize and implement a new algorithm for invariants of elementary abelian groups, see this arXiv preprint if you are curious about the math involved. The code is hosted on the InvariantRing repo (managed by Federico Galetto) and a pull request is now under review… hopefully it will be distributed with the next release of Macaulay2 in June, watch the comments for an update!

Recently, Francesca and Anna Natalie attended the Future of Macaulay2 workshop at Georgia Tech aimed at securing a long future for this open source software as long time authors Dan Grayson and Mike Stillman pass the torch to the next generation.

But, from a student’s perspective, why should one get involved with M2? What is so valuable about learning new software and technologies? Emerging scholars not only obtain math research experience, but coding and GitHub knowledge too. Anna Natalie has advanced her coding proficiency via attending various M2 workshops (including the aforementioned one). As a graduate student herself, having easy access to helpful educational resources is invaluable, and she has already started learning about PreTeXt as a possible avenue for authoring her teaching materials.

Exposure to various approaches encourages users to select methods of interaction which best suit their needs. Utilizing resources with a low barrier to entry increases a group’s productivity and potential for success. Focusing on collective understanding promotes a welcoming research environment for students and is essential to build a self-sustaining community!