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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 present the Matlab toolbox MacaulayLab, which implements numerical linear algebra algorithms for solving multivariate polynomial systems and rectangular multiparameter eigenvalue problems. Its structure and functionality are the result…

Mathematical Software · Computer Science 2026-05-21 Christof Vermeersch , Bart De Moor

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

We describe the main functions of the Macaulay2 package Quasidegrees. The purpose of this package is to compute the quasidegree set of a finitely generated A-graded module presented as the cokernel of a monomial matrix. We provide examples…

Commutative Algebra · Mathematics 2019-10-16 Roberto Barrera

We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for the cohomology groups of line bundles on the incidence…

Algebraic Geometry · Mathematics 2025-03-25 Annet Kyomuhangi , Emanuela Marangone , Claudiu Raicu , Ethan Reed

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

{\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 an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-Stillman, which concerns the standard graded BGG…

Commutative Algebra · Mathematics 2025-11-26 Maya Banks , Michael K. Brown , Tara Gomes , Prashanth Sridhar , Eduardo Torres Davila , Sasha Zotine

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

Algebraic Geometry · Mathematics 2024-03-27 Alessio Borzì

The task of voxel resolution for a space curve in video memory of 3D display is set. Furthermore, an approach solution of voxel resolution of arbitrary space curve, given in parametric form, is studied. Numerous numbers of intensive…

Graphics · Computer Science 2018-03-02 Anas M. Al-Oraiqat , E. A. Bashkov , S. A. Zori

We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global $\mathbb{A}^1$-Brouwer degrees and studying symmetric bilinear forms over the complex numbers, the real numbers, the rational numbers, and finite fields of…

Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…

Commutative Algebra · Mathematics 2019-10-16 Ben Drabkin , Eloísa Grifo , Alexandra Seceleanu , Branden Stone

Macaulay dual spaces provide a local description of an affine scheme and give rise to computational machinery that is compatible with the methods of numerical algebraic geometry. We introduce eliminating dual spaces, use them for computing…

Algebraic Geometry · Mathematics 2015-03-09 Robert Krone , Anton Leykin

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

We define the notion of "projective" multiresolution analyses, for which, by definition, the initial space corresponds to a finitely generated projective module over the algebra $C(\btn)$ of continuous complex-valued functions on an…

Functional Analysis · Mathematics 2007-05-23 Judith A. Packer , Marc A. Rieffel

Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein and Rajchgot. We introduce the Macaulay2 package…

Commutative Algebra · Mathematics 2024-03-27 Mike Cummings , Adam Van Tuyl

We present the $\textit{NumericalImplicitization}$ package for $\textit{Macaulay2}$, which allows for user-friendly computation of the invariants of the image of a polynomial map, such as dimension, degree, and Hilbert function values. This…

Algebraic Geometry · Mathematics 2019-10-16 Justin Chen , Joe Kileel

The MIGALE project (http://www.sai.msu.su/migale) provides databases and data analysis tools to study the evolution of galaxies from z=1 to z=0. It develops and maintain a general database, HyperLeda, to give a homogenized parameterization…

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

A tutorial of the Mathematica package CGAlgebra, for conformal geometric algebra calculations is presented. Using rule-based programming, the 5-dimensional conformal geometric algebra is implemented and defined functions simplify the…

Mathematical Software · Computer Science 2022-07-01 E. Alejandra Ortiz-Duran , Jose L. Aragon