Related papers: A Macaulay 2 interface for Normaliz
We present in this paper an evolution of a tool from a user interface for a concrete Computer Algebra system for Algebraic Topology (the Kenzo system), to a front-end allowing the interoperability among different sources for computation and…
We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.
We define Macaulay bases of modules, which are a common generalization of Groebner bases and Macaulay $H$-bases to suitably graded modules over a commutative graded $\mathbf{k}$-algebra, where the index sets of the two gradings may differ.…
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…
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…
This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.
In this paper, we present an algorithm for computing a fundamental matrix of formal solutions of completely integrable Pfaffian systems with normal crossings in several variables. This algorithm is a generalization of a method developed for…
In this article we show how to compute a matrix representation and the implicit equation by means of the method developed in [Botbol: arXiv:1007.3437], using the computer algebra system Macaulay2 \cite{M2}. As it is probably the most…
This introduces Rees algebras and some of their uses with illustrations via version 2.0 of the Macaulay2 package ReesAlgebra.m2.
The Macaulay2 package SumsOfSquares decomposes polynomials as sums of squares. It is based on methods to rationalize sum-of-squares decompositions due to Parrilo and Peyrl. The package features a data type for sums-of-squares polynomials,…
Reduze is a computer program for reducing Feynman integrals to master integrals employing a variant of Laporta's reduction algorithm. This article describes version 2 of the program. New features include the distributed reduction of single…
The aim of this article is to give a method to construct bimodule resolutions of associative algebras, generalizing Bardzell's well-known resolution of monomial algebras. We stress that this method leads to concrete computations, providing…
Colombeau algebras constitute a convenient framework for performing nonlinear operations like multiplication on Schwartz distributions. Many variants and modifications of these algebras exist for various applications. We present a…
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
The Weyl closure is a basic operation in algebraic analysis: it converts a system of differential operators with rational coefficients into an equivalent system with polynomial coefficients. In addition to encoding finer information on the…
We describe an algorithm for the computation of generalized (or weighted) Ehrhart series based on Stanley decompositions as implemented in the offspring NmzIntegrate of Normaliz. The algorithmic approach includes elementary proofs of the…
We construct and normalise intertwining operators at the level of Hilbert modules describing the principal series of SL(2). Normalisation is achieved through the use of a Fourier transform defined on some homogenous space and twisted by a…
In this paper we study the normality of monomial ideals using linear programming and graph theory. We give normality criteria for monomial ideals, for ideals generated by monomials of degree two, and for edge ideals of graphs and clutters…
We describe the computation of tables of Hilbert modular forms of parallel weight 2 over totally real fields.
We introduce the Macaulay2 package $\mathtt{LinearTruncations}$ for finding and studying the truncations of a multigraded module over a standard multigraded ring that have linear resolutions.