Related papers: The Rees Algebra Package in Macaulay2
A supplemental paper detailing the QuillenSuslin package for Macaulay2. The QuillenSuslin package for Macaulay2 provides the ability to compute a free basis for a projective module over a polynomial ring with coefficients in Q, Z or Z/p for…
In this short article I introduce the "jordan" package which provides functionality for working with different types of Jordan algebra. I give some numerical verification of the Jordan identity for the five types of Jordan algebras. The…
We study the defining equations of the Rees algebra of ideals arising from curve parametrizations in the plane and in rational normal scrolls, inspired by the work of Madsen and Kustin, Polini and Ulrich. The curves are related by work of…
\pkg{multiplex} is a computer program that provides algebraic tools for the analysis of multiple network structures within the \proglang{R} environment. Apart from the possibility to create and manipulate multivariate data representing…
We describe the package "IncidenceCorrespondenceCohomology" for the computer algebra system Macaulay2. The main feature concerns the computation of characters and dimensions for the cohomology groups of line bundles on the incidence…
A very elementary introduction to quantum algebras is presented and a few examples of their physical applications are mentioned.
Lie symmetry analysis provides a general theoretical framework for investigating ordinary and partial differential equations. The theory is completely algorithmic even if it usually involves lengthy computations. For this reason, many…
A short introduction to the mathematical methods and technics of differential algebras and modules adapted to the problems of mathematical and theoretical physics is presented.
Let $R=\k[x,y,z]$ and $I=(f_0,\dots,f_{n-1})$ be a height two perfect ideal which is almost linearly presented (that is, all but the last column have linear entries, but the last column has entries which are homogeneous of degree $2$).…
We are developing a Maple package of functions related to Rota's Umbral Calculus. A Mathematica version of this package is being developed in parallel.
We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…
The Jacobian algebras are introduced and their various properties are studied.
In this paper, we introduce some particular families of graphicable algebras obtained by following a relatively new line of research, initiated previously by some of the authors. It consists of the use of certain objects of Discrete…
In the present paper, we describe some experiences in using programming, commands and graphical interfaces based on computer algebra systems, as tools for learning Physics and Mathematics.
Here I present the 'clifford' package for working with Clifford algebras in the R programming language. The algebra is described and package idiom is given.
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…
The goals of this paper are threefold. First, we provide a new ''universal'' definition for the Racah algebra of rank 2 as an extension of the rank-1 Racah algebra where the generators are indexed by subsets and any three disjoint indexing…
In this paper we present Affine.m - program for computations in representation theory of finite-dimensional and affine Lie algebras and describe implemented algorithms. Algorithms are based upon the properties of weights and Weyl symmetry.…
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…
We use the theory of reductive dual pairs due to Howe to obtain explicit realizations of irreducible representations of the Yangian of the general linear Lie algebra, and of the twisted Yangians corresponding to the symplectic and…