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Related papers: Matroids: A Macaulay2 package

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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 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

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 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

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

We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove that these matroids provide a combinatorial description of…

Combinatorics · Mathematics 2024-08-06 Alheydis Geiger , Kevin Kuehn , Raluca Vlad

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 highlight some features of the SimplicialComplexes package in Macaulay2.

Commutative Algebra · Mathematics 2023-08-30 Ben Hersey , Gregory G. Smith , Alexandre Zotine

We introduce the Macaulay2 package $\mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.

Commutative Algebra · Mathematics 2023-01-25 Lauren Cranton Heller , Navid Nemati

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

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

The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any…

Algebraic Geometry · Mathematics 2018-08-28 Giovanni Staglianò

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 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

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

{\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

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 package allMarkovBases for Macaulay2, which is used to compute all minimal Markov bases of a given toric ideal. The package builds on functionality of 4ti2 by producing the fiber graph of the toric ideal. The package uses…

Commutative Algebra · Mathematics 2025-02-27 Oliver Clarke , Alexander Milner

Using the framework of pastures and foundations of matroids developed by Baker-Lorscheid, we give algorithms to: (i) compute the foundation of a matroid, and (ii) compute all morphisms between two pastures. Together, these provide an…

Combinatorics · Mathematics 2023-07-27 Tianyi Zhang , Justin Chen