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The package \texttt{NumericalCertification} implements methods for certifying numerical approximations of solutions for a given system of polynomial equations. For certifying regular solutions, the package implements Smale's $\alpha$-theory…

Numerical Analysis · Mathematics 2022-08-04 Kisun Lee

In this paper, we discuss the integer decomposition property for Cayley sums and Minkowski sums of lattice polytopes. In fact, we characterize when Cayley sums have the integer decomposition property in terms of Minkowski sums. Moreover, by…

Combinatorics · Mathematics 2023-07-14 Akiyoshi Tsuchiya

We describe a Maple package that serves at least four purposes. First, one can use it to compute whether or not a given polyhedral structure is Zometool constructible. Second, one can use it to manipulate Zometool objects, for example to…

Computational Geometry · Computer Science 2021-04-05 Benoit Charbonneau , Spencer Whitehead

We present the python package DiPolMol-Py, which can be used to calculate the rotational and hyperfine structure of $^2\Sigma$ molecules. The calculations can be performed in the presence of dc magnetic fields, dc electric fields and far…

Atomic Physics · Physics 2025-09-01 Bethan Humphreys , Alex J. Matthies , Hannah J. Williams

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,…

This is an expository version of our paper [arXiv:1902.07384]. Our aim is to present recent Macaulay2 algorithms for computation of mixed multiplicities of ideals in a Noetherian ring which is either local or a standard graded algebra over…

Commutative Algebra · Mathematics 2023-07-20 Kriti Goel , Vivek Mukundan , Sudeshna Roy , J. K. Verma

The \texttt{StronglyStableIdeals} package for \textit{Macaulay2} provides a method to compute all saturated strongly stable ideals in a given polynomial ring with a fixed Hilbert polynomial. A description of the main method and auxiliary…

Symbolic Computation · Computer Science 2019-10-16 Davide Alberelli , Paolo Lella

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

We report on a package of routines for the computer algebra system Maple which supports the explicit determination of the geometric quantities, field equations, equations of motion, and conserved quantities of General Relativity in the…

General Relativity and Quantum Cosmology · Physics 2007-05-23 Dirk Puetzfeld

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 article mainly presents some results in using MAPLE platform for computer algebra and GrTensorII package in doing calculations for theoretical and numerical cosmology

Symbolic Computation · Computer Science 2007-05-23 Dumitru N. Vulcanov , Valentina D. Vulcanov

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 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

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

Lattice polytope representation of natural numbers is introduced based on the fundamental theorem of arithmetic. The combinatorial and geometric properties of the polytopes are studied using Polymake and Qhull software. The volume of the…

General Mathematics · Mathematics 2020-03-23 Ya-Ping Lu , Shu-Fang Deng

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 introduce the package combinatorics for the software CoCoA. This package provides a data structure and the necessary methods for computing several known enumerative combinatorial invariants.

Combinatorics · Mathematics 2026-02-16 Akin Scott , Michele Torielli

We present our implementation of an algorithm which functions as a numerical oracle for the Newton polytope of a hypersurface in the Macaulay2 package NumericalNP.m2. We propose a tropical membership test, relying on this algorithm, for…

Algebraic Geometry · Mathematics 2018-11-30 Taylor Brysiewicz

This paper studies the structure of Lax pairs associated with integrable lattice systems (where space is a one-dimensional lattice, and time is continuous). It describes a procedure for generating examples of such systems, and emphasizes…

solv-int · Physics 2015-06-26 R. S. Ward

We introduce the AdditiveToricVarieties package for Macaulay2, a software system for algebraic geometry and commutative algebra, with methods for working with additive group actions on complete toric varieties. More precisely, we implement…

Algebraic Geometry · Mathematics 2026-02-25 Fabián Levicán-Santibáñez , Pedro Montero