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

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…

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 versal deformation of two-dimensional cyclic quotient singularities in terms of equations, following Arndt, Brohme and Hamm. For the reduced components the equations are determined by certain systems of dots in a triangle.…

Algebraic Geometry · Mathematics 2009-06-09 Jan Stevens

A rather complete phenomenology of the singularities is developed according to a new algebraic point of view in the frame of Langlands global correspondences. That is to say,a process of: -singularizations and versal deformations of these,…

Representation Theory · Mathematics 2007-05-23 Christian Pierre

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

We present the Macaulay2 package Resultants, which provides commands for the effective computation of multivariate resultants, discriminants, and Chow forms. We provide some background for the algorithms implemented and show, with a few…

Algebraic Geometry · Mathematics 2018-08-28 Giovanni Staglianò

In this article, we discuss formal invariants of singularly-perturbed linear differential systems in neighborhood of turning points and give algorithms which allow their computation. The algorithms proposed are implemented in the computer…

Classical Analysis and ODEs · Mathematics 2016-12-15 Moulay A. Barkatou , Suzy S. Maddah

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 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

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 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

We develop deformation theory of algebras over quadratic operads where the parameter space is a commutative local algebra. We also give a construction of a distinguised deformation of an algebra over a quadratic operad with a complete local…

K-Theory and Homology · Mathematics 2013-11-08 Alice Fialowski , Goutam Mukherjee , Anita Naolekar

We give a computational algorithm for computing Ext groups between bounded complexes of coherent sheaves on a projective variety, and we describe an implementation of this algorithm in Macaulay2. In particular, our results yield methods for…

Algebraic Geometry · Mathematics 2025-09-30 Michael K. Brown , Souvik Dey , Guanyu Li , Mahrud Sayrafi

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

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 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

We describe a significant update to the Macaulay2 package A1BrouwerDegrees. We extend several methods in the previous version of the package to the setting of finite \'{e}tale algebras, allowing the computation of transfers along finite…

The paper introduces the software Spectangular for spectral disentangling via singular value decomposition with global optimisation of the orbital parameters of the stellar system or radial velocities of the individual observations. We will…

Instrumentation and Methods for Astrophysics · Physics 2017-01-18 Daniel P. Sablowski , Michael Weber

The purpose of this paper is to study global deformations of Hom-Leibniz algebras. We introduce a cohomology for Hom-Leibniz algebras with values in a Hom-module, characterize versal deformations and provide examples.

Rings and Algebras · Mathematics 2013-03-01 Faouzi Ammar , Zeyneb Ejbehi , Abdenacer Makhlouf