Related papers: Elimination Templates in Macaulay2
This short paper presents saturation-based algorithms for homogenization and elimination. This algorithm can compute elimination ideals by using syzygies and ideal membership test, hence it works with any} monomial order, in particular…
Using discrete Morse theory, Batzies and Welker introduced Morse resolutions of monomial ideals. In this note, we present the {\it Macaulay2} package {\tt MorseResolutions} for working with two important classes of Morse resolutions:…
Using the geometric vertex decomposition property first defined by Knutson, Miller, and Yong, a recursive definition for geometrically vertex decomposable ideals was given by Klein and Rajchgot. We introduce the Macaulay2 package…
We introduce the Macaulay2 package GradedLieAlgebras for doing computations in graded Lie algebras presented by generators and relations.
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.
We present here an overview of the hypermatrix spectral decomposition deduced from the Bhattacharya-Mesner hypermatrix algebra. We describe necessary and sufficient conditions for the existence of a spectral decomposition. We further extend…
We introduce the package "GraphicalModelsMLE" for computing the maximum likelihood estimates (MLEs) of a Gaussian graphical model in the computer algebra system Macaulay2. This package allows the computation of MLEs for the class of…
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…
We highlight some features of the SimplicialComplexes package in Macaulay2.
An algorithm for resolution of singularities in characteristic zero is described. It is expressed in terms of multi-ideals, that essentially are defined as a finite sequence of pairs, each one consiting of a sheaf of ideals and a positive…
We introduce the $\textit{Macaulay2}$ package $\texttt{OIGroebnerBases}$ for working with OI-modules over Noetherian polynomial OI-algebras. The main methods implement OI-analogues of Buchberger's algorithm and Schreyer's theorem to compute…
Elimination of unknowns in a system of differential equations is often required when analysing (possibly nonlinear) dynamical systems models, where only a subset of variables are observable. One such analysis, identifiability, often relies…
We introduce a package for doing tropical computations in Macaulay2. The package draws on the functionality of Gfan and Polymake while making the process as simple as possible for the end user. This provides a powerful and user friendly…
Numerical Algebraic Geometry uses numerical data to describe algebraic varieties. It is based on the methods of numerical polynomial homotopy continuation, an alternative to the classical symbolic approaches of computational algebraic…
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…
We provide an overview of the Macaulay2 package VersalDeformations, which algorithmically computes versal deformations of isolated singularities, as well as local (multi)graded Hilbert schemes.
Large eliminations provide an expressive mechanism for arity- and type-generic programming. However, as large eliminations are closely tied to a type theory's primitive notion of inductive type, this expressivity is not expected within…
We introduce a new Macaulay2 package, Nauty, which gives access to powerful methods on graphs provided by the software nauty by Brendan McKay. The primary motivation for accessing nauty is to determine if two graphs are isomorphic. We also…
Recently Gouveia, Thomas and the authors introduced the slack realization space, a new model for the realization space of a polytope. It represents each polytope by its slack matrix, the matrix obtained by evaluating each facet inequality…
We describe a general approach for computing generators for elimination ideals associated with matrix and hypermatrix spectral decomposition constraints. We derive from these generators iterative procedures for approximating the spectral…