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

The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure. These techniques are numerically stable, and can be used…

Commutative Algebra · Mathematics 2014-05-22 Robert Krone

We describe the computer algebra software package SpectralSequences for the computer algebra system Macaulay2. This package implements many data types, objects and algorithms which pertain to, among other things, filtered complexes,…

Commutative Algebra · Mathematics 2016-10-19 Adam Boocher , Nathan Grieve , Eloísa Grifo

We introduce a new Macaulay 2 package, SimplicialDecomposability, which works in conjunction with the extant package SimplicialComplexes in order to compute a shelling order, if one exists, of a specified simplicial complex. Further,…

Combinatorics · Mathematics 2010-08-23 David Cook

We introduce the Macaulay2 package SparseResultants, which provides general tools for computing sparse resultants, sparse discriminants, and hyperdeterminants. We give some background on the theory and briefly show how the package works.

Algebraic Geometry · Mathematics 2021-09-02 Giovanni Staglianò

The MultiplicitySequence package for Macaulay2 computes the multiplicity sequence of a graded ideal in a standard graded ring over a field, as well as several invariants of monomial ideals related to integral dependence. We discuss two…

Commutative Algebra · Mathematics 2024-03-27 Justin Chen , Youngsu Kim , Jonathan Montaño

We introduce a package for doing tropical computations in Macaulay2. The package draws on the functionality of Gfan and Polymake while making the process as simple as possible for the end user. This provides a powerful and user friendly…

{\tt AbstractSimplicialComplexes.m2} is a computer algebra package written for the computer algebra system {\tt Macaulay2} \cite{M2}. It provides new infrastructure to work with abstract simplicial complexes and related homological…

Algebraic Geometry · Mathematics 2025-04-15 Nathan Grieve

We give a description of a new Macaulay2 package called SimplicialPosets. This package provides functions for working with simplicial posets and calculating their generalized Stanley-Reisner ideals. For practical purposes, we also introduce…

Combinatorics · Mathematics 2021-01-05 Nathan Nichols

We introduce the Macaulay2 package MatchingPowers. It allows to compute and manipulate the matching powers of a monomial ideal. The basic theory of matching powers is explained and the main features of the package are presented.

Commutative Algebra · Mathematics 2023-12-21 Antonino Ficarra

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

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

This article highlights the ToricHigherDirectImages package in Macaulay2. The central feature is a method for computing (higher) direct images of line bundles under surjective toric morphisms.

Algebraic Geometry · Mathematics 2025-05-30 Sasha Zotine

This note introduces the $\texttt{LikelihoodGeometry}$ package for the computer algebra system $\textit{Macaulay2}$. This package gives tools to construct the likelihood correspondence of a discrete algebraic statistical model, a variety…

Computation · Statistics 2024-11-19 David Barnhill , John Cobb , Matthew Faust

We introduce the Brackets package for the computer algebra system Macaulay2, which provides convenient syntax for computations involving the classical invariants of the special linear group. We describe our implementation of bracket rings…

Algebraic Geometry · Mathematics 2025-04-02 Dalton Bidleman , Timothy Duff , Jack Kendrick , Michael Zeng

This note introduces the Macaulay2 package SchurVeronese, which gathers together data about Veronese syzygies and makes it readily accessible in Macaulay2. In addition to standard Betti tables, the package includes information about the…

Commutative Algebra · Mathematics 2022-03-09 Juliette Bruce , Daniel Erman , Steve Goldstein , Jay Yang

The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $\alpha$-theory…

Numerical Analysis · Mathematics 2022-08-04 Kisun Lee

Normaliz is a tool for the computation of Hilbert bases of normal affine monoids and related tasks. We describe the Macaulay 2 interface to Normaliz. It makes Normaliz accessible for operations on monoid algebras in Macaulay 2 and,…

Commutative Algebra · Mathematics 2010-08-16 Winfried Bruns , Gesa Kaempf

We introduce the Macaulay2 package HomologicalShiftIdeals. It allows to compute the homological shift ideals of a monomial ideal, and to check the homological shift properties, including having linear resolution, having linear quotients, or…

Commutative Algebra · Mathematics 2023-09-19 Antonino Ficarra