Related papers: A computer algebra system for R: Macaulay2 and the…
The NumericalHilbert package for Macaulay2 includes algorithms for computing local dual spaces of polynomial ideals, and related local combinatorial data about its scheme structure. These techniques are numerically stable, and can be used…
Algebraic statistics is concerned with the study of probabilistic models and techniques for statistical inference using methods from algebra and geometry. This article presents a list of open mathematical problems in this emerging field,…
Algebraic computing in relativity and gravitation dates back more than thirty years, but only relatively recently has hardware of sufficient power to tackle large scale calculations become commonplace. Whereas it is generally understood…
In the last quarter of a century, algebraic statistics has established itself as an expanding field which uses multilinear algebra, commutative algebra, computational algebra, geometry, and combinatorics to tackle problems in mathematical…
We describe the Macaulay2 package "A1BrouwerDegrees" for computing local and global $\mathbb{A}^1$-Brouwer degrees and studying symmetric bilinear forms over the complex numbers, the real numbers, the rational numbers, and finite fields of…
Despite several deficiencies, the use of spreadsheets in statistics courses is increasingly common. In this paper we discuss many shortcomings resulting from this approach. We suggest a technique integrating a spreadsheet and a dedicated…
\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…
Solving a system of polynomial equations is a ubiquitous problem in the applications of mathematics. Until recently, it has been hopeless to find explicit solutions to such systems, and mathematics has instead developed deep and powerful…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
Maximum likelihood estimation (MLE) is a fundamental problem in statistics. Characteristics of the MLE problem for discrete algebraic statistical models are reflected in the geometry of the $\textit{likelihood correspondence}$, a variety…
In the last decade, developments in tropical geometry have provided a number of uses directly applicable to problems in statistical learning. The TML package is the first R package which contains a comprehensive set of tools and methods…
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…
This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…
We describe a new software package for computing multiplier ideals in certain cases, including monomial ideals, monomial curves, generic determinantal ideals, and hyperplane arrangements. In these cases we take advantage of combinatorial…
It is shown how to set up, conduct, and analyze large simulation studies with the new R package simsalapar = simulations simplified and launched parallel. A simulation study typically starts with determining a collection of input variables…
Even though in recent years the scale of statistical analysis problems has increased tremendously, many statistical software tools are still limited to single-node computations. However, statistical analyses are largely based on dense…
The Macaulay2 package Cremona performs some computations on rational and birational maps between irreducible projective varieties. For instance, it provides methods to compute degrees and projective degrees of rational maps without any…
We introduce a Macaulay2 package for working with jet schemes. The main method constructs jets of ideals, polynomial rings and their quotients, ring homomorphisms, affine varieties, and (hyper)graphs. The package also includes additional…
The following article is an application of commutative algebra to the study of multiparameter persistent homology in topological data analysis. In particular, the theory of finite free resolutions of modules over polynomial rings is applied…
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.