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We introduce the MatrixSchubert package for the computer algebra system Macaulay2. This package has tools to construct and study matrix Schubert varieties and alternating sign matrix (ASM) varieties. The package also introduces tools for…

Algebraic Geometry · Mathematics 2025-11-26 Ayah Almousa , Sean Grate , Daoji Huang , Patricia Klein , Adam LaClair , Yuyuan Luo , Joseph McDonough

We introduce the package \texttt{EliminationTemplates} for the Macaulay2 computer algebra system, which provides tools for constructing automatic solvers for families of zero-dimensional radical ideals depending on algebraically independent…

Commutative Algebra · Mathematics 2026-05-06 Manav Batavia , Cheng Chen , Anna Natalie Chlopecki , Timothy Duff , William Huang , Aolong Li , Wanchun Shen

The {\tt Macaulay2} package {\tt RandomMonomialIdeals} provides users with a set of tools that allow for the systematic generation and study of random monomial ideals. It also introduces new objects, Sample and Model, to allow for…

Commutative Algebra · Mathematics 2019-10-16 Sonja Petrović , Despina Stasi , Dane Wilburne

The article presents an algebra to represent two dimensional patterns using reciprocals of polynomials. Such a representation will be useful in neural network training and it provides a method of training patterns that is much more…

Information Theory · Computer Science 2011-02-23 Subhash Kak

The Macaulay2 package DecomposableSparseSystems implements methods for studying and numerically solving decomposable sparse polynomial systems. We describe the structure of decomposable sparse systems and explain how the methods in this…

Algebraic Geometry · Mathematics 2021-07-21 Taylor Brysiewicz , Jose Israel Rodriguez , Frank Sottile , Thomas Yahl

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…

Commutative Algebra · Mathematics 2024-03-27 Luigi Ferraro , Federico Galetto , Francesca Gandini , Hang Huang , Matthew Mastroeni , Xianglong Ni

In this article, we present FastMinors.m2, a package in Macaulay2 designed to introduce new methods focused on computations in function field linear algebra. Some key functionality that our package offers includes: finding a submatrix of a…

Commutative Algebra · Mathematics 2023-08-30 Boyana Martinova , Marcus Robinson , Karl Schwede , Yuhui Yao

We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties, and (hyper)graphs. The package also includes additional…

Commutative Algebra · Mathematics 2023-01-25 Federico Galetto , Nicholas Iammarino

We explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{g}$ (typically $\mathfrak{sl}_n$) and a…

Algebraic Geometry · Mathematics 2025-11-26 Luke Oeding

We introduce a new Macaulay2 package, Nauty, which gives access to powerful methods on graphs provided by the software nauty by Brendan McKay. The primary motivation for accessing nauty is to determine if two graphs are isomorphic. We also…

Combinatorics · Mathematics 2011-04-27 David Cook

The free algebra is an interesting and useful algebraic object. Here I introduce "freealg", an R package which furnishes computational support for free algebras. The package uses the standard template library's "map" class for efficiency,…

Symbolic Computation · Computer Science 2022-11-09 Robin K. S. Hankin

We present {\tt RandomPoints}, a package in \emph{Macaulay2} designed mainly to identify rational and geometric points in a variety over a finite field. We provide tools to estimate the dimension of a variety. We also present methods to…

Algebraic Geometry · Mathematics 2023-08-30 Sankhaneel Bisui , Zhan Jiang , Sarasij Maitra , Thái Thành Nguyên , Karl Schwede

We present the Macaulay2 package TropicalToric.m2 for toric intersection theory computations using tropical geometry.

Algebraic Geometry · Mathematics 2024-03-27 Alessio Borzì

We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subagebra bases -- which are also known as…

Commutative Algebra · Mathematics 2024-06-05 Michael Burr , Oliver Clarke , Timothy Duff , Jackson Leaman , Nathan Nichols , Elise Walker

This note describes a Macaulay2 package for handling divisors. Group operations for divisors are included. There are methods for converting divisors to reflexive or invertible sheaves. Additionally, there are methods for checking whether…

Algebraic Geometry · Mathematics 2019-06-25 Karl Schwede , Zhaoning Yang

We describe a Macaulay2 package for computing Schur complexes. This package expands on the ChainComplexOperations package by David Eisenbud.

We present the Macaulay2 package Resultants, which provides commands for the effective computation of multivariate resultants, discriminants, and Chow forms. We provide some background for the algorithms implemented and show, with a few…

Algebraic Geometry · Mathematics 2018-08-28 Giovanni Staglianò

We introduce the CpMackeyFunctors package for Macaulay2, which allows for computations with Mackey functors over a cyclic group of prime order.

Algebraic Topology · Mathematics 2025-09-09 Thomas Brazelton , David Chan , Benjamin Mudrak , Ben Spitz , Chase Vogeli , Chenglu Wang , Michael R. Zeng , Sasha Zotine

In this short note, we provide OPEs for several affine W-algebras associated with Lie algebras of rank two and give some direct applications.

Mathematical Physics · Physics 2022-11-18 Justine Fasquel

In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…