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Related papers: RationalMaps, a package for Macaulay2

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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 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

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 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

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

This note describes a \emph{Macaulay2} package for computations in prime characteristic commutative algebra. This includes Frobenius powers and roots, $p^{-e}$-linear and $p^{e}$-linear maps, singularities defined in terms of these maps,…

A rational map whose source and image are projectively embedded varieties has an {\em Arithmetically Cohen-Macaulay graph} if the Rees algebra of one (hence any) of its base ideals is a Cohen-Macaulay ring. If the map is birational onto the…

Algebraic Geometry · Mathematics 2017-01-19 S. Hamid Hassanzadeh , Aron Simis

We provide new examples of integrable rational maps in four dimensions with two rational invariants, which have unexpected geometric properties, as for example orbits confined to non algebraic varieties, and fall outside classes studied by…

Exactly Solvable and Integrable Systems · Physics 2018-11-06 N. Joshi , CM. Viallet

Symbolic powers are a classical commutative algebra topic that relates to primary decomposition, consisting, in some circumstances, of the functions that vanish up to a certain order on a given variety. However, these are notoriously…

Commutative Algebra · Mathematics 2019-10-16 Ben Drabkin , Eloísa Grifo , Alexandra Seceleanu , Branden Stone

In this Macaulay2 \cite{M2} package we define an object called {\it linear code}. We implement functions that compute basic parameters and objects associated with a linear code, such as generator and parity check matrices, the dual code,…

We describe a recently revived version of the software package SubalgberaBases, which is distributed in the Macaulay2 computer algebra system. The package allows the user to compute and manipulate subagebra bases -- which are also known as…

Commutative Algebra · Mathematics 2024-06-05 Michael Burr , Oliver Clarke , Timothy Duff , Jackson Leaman , Nathan Nichols , Elise Walker

Numerical algebraic geometry is the field of computational mathematics concerning the numerical solution of polynomial systems of equations. Bertini, a popular software package for computational applications of this field, includes…

Algebraic Geometry · Mathematics 2013-10-15 Daniel J. Bates , Elizabeth Gross , Anton Leykin , Jose Israel Rodriguez

We introduce the CpMackeyFunctors package for Macaulay2, which allows for computations with Mackey functors over a cyclic group of prime order.

Algebraic Topology · Mathematics 2025-09-09 Thomas Brazelton , David Chan , Benjamin Mudrak , Ben Spitz , Chase Vogeli , Chenglu Wang , Michael R. Zeng , Sasha Zotine

We give an overview of a Macaulay2 package for computing with the multigraded BGG correspondence. This software builds on the package BGG due to Abo-Decker-Eisenbud-Schreyer-Smith-Stillman, which concerns the standard graded BGG…

Commutative Algebra · Mathematics 2025-11-26 Maya Banks , Michael K. Brown , Tara Gomes , Prashanth Sridhar , Eduardo Torres Davila , Sasha Zotine

Cellular resolutions are a technique for constructing resolutions of monomial ideals by giving a cell complex labeled by monomials, or more generally, by monomial modules. This \verb|Macaulay2| package allows us to work with cellular…

Commutative Algebra · Mathematics 2023-07-18 Aleksandra Sobieska , Jay Yang

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

Algebraic methods have a long history in statistics. The most prominent manifestation of modern algebra in statistics can be seen in the field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to…

Computation · Statistics 2017-06-27 David Kahle , Christopher O'Neill , Jeff Sommars

A program package, which facilitates computations in the framework of Analytic approach to QCD, is developed and described in details. The package includes the explicit expressions for relevant spectral functions calculated up to the…

High Energy Physics - Phenomenology · Physics 2014-11-20 A. V. Nesterenko , C. Simolo

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

The paper presents a software tool for analysis and interactive engagement in various logical reasoning tasks. A first feature of the program consists in providing an interface for working with logic-specific repositories of formal…

Computers and Society · Computer Science 2015-07-15 Ştefan Minică