caracas: Computer Algebra

title: 'caracas: Computer algebra in R' authors: - affiliation: 1 name: Mikkel Meyer Andersen orcid: 0000-0002-0234-0266 - affiliation: 1 name: Søren Højsgaard orcid: 0000-0002-3269-9552 date: "22 June 2021" bibliography: paper.bib tags: - cas - mathematics - symbolic mathematics - statistics - tex - latex affiliations: - index: 1 name: Department of Mathematical Sciences, Aalborg University, Denmark

Summary

caracas is an R [@R] package that enables a computer algebra system (CAS) within R via the open source Python CAS SymPy [@sympy], which is made possible via reticulate [@reticulate]. caracas is published at The Comprehensive R Archive Network (CRAN) [@R] at https://cran.r-project.org/package=caracas, its source is available at https://github.com/r-cas/caracas and the documentation is available at https://r-cas.github.io/caracas/.

Much work went into integrating caracas into R such that caracas behaves much like other R libraries and objects.

caracas contains a number of vignettes demonstrating both basic functionality like solving equations as well as more advanced tasks like finding the concentration and covariance matrix in a dynamic linear model.

Compared to other CAS R packages like Ryacas [@Andersen2019] based on yacas [@yacas;@Pinkus2002], caracas is more feature complete, for example with respect to solving equations.

Statement of Need

From a statistician's perspective, R is excellent for data handling, graphics, for model fitting and statistical inference and as a programming environment. However, R largely lacks the ability to perform symbolic computations. That is, R only supports to a small extent the step from posing a problem (for example a model) in mathematical terms over symbolic manipulations of the model and further onto a stage where a model can be combined with data. The caracas provides capabilities for these steps directly in R. Topics that can be handled in caracas include:

Sums,
limits,
integration,
differentiation,
symbolic matrices and vectors,
simplification of mathematical expressions and
outputting in TeX format.

Several (commercial) systems are available for such tasks (and many more), e.g. Mathematica [@Mathematica] and Maple [@Maple]. However, we will argue that there is a virtue in being able to handle such tasks directly from within R using the familiar R syntax. Moreover, it is an integrated part of the design of caracas that it is straightforward to coerce a mathematical object into an R expression which can, e.g., be evaluated numerically.

Acknowledgements

We would like to thank the R Consortium for financial support for creating the caracas package (link to details on the funded project) and to users for pinpointing points that can be improved in caracas.