A Computer Algebra System for R: Macaulay2 and the m2r Package

Abstract

Algebraic methods have a long history in statistics. Apart from the ubiquitous applications of linear algebra, the most visible manifestations of modern algebra in statistics are found in the young field of algebraic statistics, which brings tools from commutative algebra and algebraic geometry to bear on statistical problems. Now over two decades old, algebraic statistics has applications in a wide range of theoretical and applied statistical domains. Nevertheless, algebraic statistical methods are still not mainstream, mostly due to a lack of easy off-the-shelf implementations. In this article we debut m2r, an R package that connects R to Macaulay2 through a persistent back-end socket connection running locally or on a cloud server. Topics range from basic use of m2r to applications and design philosophy.

Generation of all randomizations using circuits

“…However, all the contrast matrices illustrated in this paper have been processed by 4ti2 in less than 0.1 seconds. 4ti2 is now available also within the symbolic software Macaulay2, see Grayson and Stillman ( 2019 ), and there are R packages available which allow the communication between R and Macaulay2, leading to a flexible use of the symbolic computations into statistical analysis, see Kahle et al ( 2020 ).…”