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Related papers: Simplicial complexes in Macaulay2

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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

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

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 the DeterminantalRepresentations package for Macaulay2, which computes definite symmetric determinantal representations of real polynomials. We focus on quadrics and plane curves of low degree (i.e. cubics and quartics). Our…

Algebraic Geometry · Mathematics 2020-02-12 Justin Chen , Papri Dey

We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.

Algebraic Geometry · Mathematics 2022-03-09 Giovanni Staglianò

We introduce the VirtualResolution package for the computer algebra system Macaulay2. This package has tools to construct, display, and study virtual resolutions for products of projective spaces. The package also has tools for generating…

Algebraic Geometry · Mathematics 2021-01-27 Ayah Almousa , Juliette Bruce , Michael C. Loper , Mahrud Sayrafi

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 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 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

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 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

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

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

The Macaulay2 package PHCpack.m2 provides an interface to PHCpack, a general-purpose polynomial system solver that uses homotopy continuation. The main method is a numerical blackbox solver which is implemented for all Laurent systems. The…

Algebraic Geometry · Mathematics 2012-10-11 Elizabeth Gross , Sonja Petrović , Jan Verschelde

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

simpcomp is an extension (a so called package) to GAP, the well known system for computational discrete algebra. The package enables the user to compute numerous properties of (abstract) simplicial complexes, provides functions to construct…

Combinatorics · Mathematics 2019-10-24 Felix Effenberger , Jonathan Spreer

The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective…

Algebraic Geometry · Mathematics 2013-01-21 Christine Jost

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

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 Macaulay2 package SCMAlgebras. It provides functions for computing the modules of deficiency and the filter ideals, in order to check whether a module or an ideal is sequentially Cohen-Macaulay. After the basic algebraic…

Commutative Algebra · Mathematics 2025-06-10 Ernesto Lax