Related papers: A computer algebra system for R: Macaulay2 and the…
With recent dramatic increases in AI system capabilities, there has been growing interest in utilizing machine learning for reasoning-heavy, quantitative tasks, particularly mathematics. While there are many resources capturing mathematics…
Many recent statistical applications involve inference under complex models, where it is computationally prohibitive to calculate likelihoods but possible to simulate data. Approximate Bayesian Computation (ABC) is devoted to these complex…
Traditionally, statistical computing courses have taught the syntax of a particular programming language or specific statistical computation methods. Since the publication of Nolan and Temple Lang (2010), we have seen a greater emphasis on…
This article presents some aspects and experience in the use of algebraic manipulation software applied to general relativity. Some years ago certain results were reported using computer algebra platforms, but the growing popularity of…
We shortly describe the algorithms behind some of the functions provided by the Macaulay2 package MultiprojectiveVarieties, a package for multi-projective varieties and rational maps between them.
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.
We introduce T2Ku, an open source project that aims at building a semantic wiki of mathematics featuring automated reasoning(AR) techniques. We want to utilize AR techniques in a way that truly helps mathematical researchers solve problems…
Although the performance of commodity computers has improved drastically with the introduction of multicore processors and GPU computing, the standard R distribution is still based on single-threaded model of computation, using only a small…
This paper outlines our ideas on how to teach linear algebra in a mechanized mathematical environment, and discusses some of our reasons for thinking that this is a better way to teach linear algebra than the ``old fashioned way''. We…
This article introduces 'cpp11armadillo', a new R package that integrates the powerful Armadillo C++ library for linear algebra into the R programming environment. Targeted primarily at social scientists and other non-programmers, this…
Markov random fields on two-dimensional lattices are behind many image analysis methodologies. mrf2d provides tools for statistical inference on a class of discrete stationary Markov random field models with pairwise interaction, which…
Calendars are broadly used in society to display temporal information, and events. This paper describes a new R package with functionality to organize and display temporal data, collected on sub-daily resolution, into a calendar layout. The…
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be…
The Macaulay2 package CharacteristicClasses provides commands for the computation of the topological Euler characteristic, the degrees of the Chern classes and the degrees of the Segre classes of a closed subscheme of complex projective…
In this article, we describe the theoretical foundations of the Macaulay2 package ConnectionMatrices and explain how to use it. For a left ideal in the Weyl algebra that is of finite holonomic rank, we implement the computation of the…
In this paper, we introduce the fundamental notion of a Markov basis, which is one of the first connections between commutative algebra and statistics. The notion of a Markov basis is first introduced by Diaconis and Sturmfels (1998) for…
We introduce the Macaulay2 package MatchingPowers. It allows to compute and manipulate the matching powers of a monomial ideal. The basic theory of matching powers is explained and the main features of the package are presented.
The $M_2$ variables are devised to extend $M_{T2}$ by promoting transverse masses to Lorentz-invariant ones and making explicit use of on-shell mass relations. Unlike simple kinematic variables such as the invariant mass of visible…
Large networks of queueing systems model important real-world systems such as MapReduce clusters, web-servers, hospitals, call centers and airport passenger terminals. To model such systems accurately, we must infer queueing parameters from…
This note introduces the Macaulay2 package SchurVeronese, which gathers together data about Veronese syzygies and makes it readily accessible in Macaulay2. In addition to standard Betti tables, the package includes information about the…