English
Related papers

Related papers: Linear Truncations Package for Macaulay2

200 papers

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

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

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

We highlight some features of the SimplicialComplexes package in Macaulay2.

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

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…

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

CylindricalAlgebraicDecomposition.m2 is the first implementation of Cylindrical Algebraic Decomposition (CAD) in Macaulay2. CAD decomposes space into 'cells' where input polynomials are sign-invariant. This package computes an Open CAD…

Symbolic Computation · Computer Science 2025-04-01 Corin Lee , Tereso del Río , Hamid Rahkooy

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 highly anticipated use of quantum computers is the simulation of complex quantum systems including molecules and other many-body systems. One promising method involves directly applying a linear combination of unitaries (LCU) to…

Quantum Physics · Physics 2022-02-02 Richard Meister , Simon C. Benjamin , Earl T. Campbell

{\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

Using the dual of Bousfield-Friedlander localization we colocalize resolution model structures on cosimplicial objects over a left proper model category to get truncated resolution model structures. These are useful to study realization and…

Algebraic Topology · Mathematics 2007-09-27 Georg Biedermann

We extend recent results in order to construct projective resolutions for modules over twisted tensor products of truncated polynomial rings. We begin by taking note of the conditions necessary to think of these algebras as a type of Ore…

Rings and Algebras · Mathematics 2020-04-24 Dustin McPhate

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

We introduce the ForeignFunctions package for Macaulay2, which uses libffi to provide the ability to call functions from external libraries without needing to link against them at compile time. As examples, we use the library FFTW to…

Algebraic Geometry · Mathematics 2025-01-22 Douglas A. Torrance

We explain a Macaulay2 implementation of a construction, which appeared in [Holweck-Oeding arXiv:2206.13662], of a graded algebra structure on the direct sum of a Lie algebra $\mathfrak{g}$ (typically $\mathfrak{sl}_n$) and a…

Algebraic Geometry · Mathematics 2025-11-26 Luke Oeding

This article introduces the package MatchingFields for Macaulay2 and highlights some open problems. A matching field is a combinatorial object whose data encodes a candidate toric degeneration of a Grassmannian or partial flag variety of…

Combinatorics · Mathematics 2023-06-19 Oliver Clarke

This short note provides a quick introduction to relative canonical resolutions of curves on rational normal scrolls. We present our Macaulay2-package which computes the relative canonical resolution associated to a curve and a pencil of…

Algebraic Geometry · Mathematics 2021-01-27 Christian Bopp , Michael Hoff

Small and wide angle x-ray scattering tensor tomography are powerful methods for studying anisotropic nanostructures in a volume-resolved manner, and are becoming increasingly available to users of synchrotron facilities. The analysis of…

Materials Science · Physics 2025-04-24 Leonard C. Nielsen , Mads Carlsen , Sici Wang , Arthur Baroni , Torne Tänzer , Marianne Liebi , Paul Erhart

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 Lagrange2D, a Mathematica package for analysis and characterization of complex fluid flows using Lagrangian transport metrics. Lagrange2D includes built-in functions for integrating ensembles of trajectories subject to…

Fluid Dynamics · Physics 2019-08-05 William Gilpin