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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 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

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 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

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

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 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

This is the Hadamard package for Macaulay2 which computes the Hadamard product of projective subvarieties.

Algebraic Geometry · Mathematics 2020-12-21 Iman Bahmani Jafarloo

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 introduce the package LatticePolytopes for Macaulay2. The package provides methods for computations related to Cayley structures, local positivity and smoothness for lattice polytopes.

Algebraic Geometry · Mathematics 2015-11-11 Anders Lundman , Gustav Sædén Ståhl

This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.

Algebraic Geometry · Mathematics 2023-01-25 C. J. Bott , S. Hamid Hassanzadeh , Karl Schwede , Daniel Smolkin

This note describes a package for computing seminormalization of rings within Macaulay2.

Commutative Algebra · Mathematics 2020-02-12 Karl Schwede , Bernard Serbinowski

Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…

Algebraic Geometry · Mathematics 2011-11-23 Anton Leykin

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 introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.

Rings and Algebras · Mathematics 2021-01-27 Clas Löfwall , Samuel Lundqvist

The toric Hilbert scheme parametrizes all algebras isomorphic to a given semigroup algebra as a multigraded vectorspace. All components of the scheme are toric varieties, and among them, there is a fairly well understood coherent component.…

Algebraic Geometry · Mathematics 2007-05-23 Michael Stillman , Bernd Sturmfels , Rekha R. Thomas

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

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 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…