MAXIMA: An open source computer algebra system

In one way or another, economists, especially econometricians, wind up spending a good part of their day interacting with computers. We may find ourselves writing Monte Carlo simulations designed to study the finite-sample behaviour of statistical procedures, conducting applied data analysis and visualization, or conducting mathematical analysis with the aid of symbolic mathematical software. Most are aware of the renowned open source GNU compiler collection (gcc.gnu.org), which is useful for low-level programming in, say, Fortran or C, while the profession has embraced R, which is an open source high-level language and environment for statistical computing and graphics; see www.R-project.org or Racine and Hyndman (2002) for further information. However, until recently, the availability of a tested and powerful platform for symbolic mathematics was notably absent from the open source arena. Maxima is a computer algebra package that has a variety of potential uses for economists and econometricians alike. It can be used to manipulate symbolic and numerical expressions including differentiation, integration, Taylor series, Laplace transforms, ordinary differential equations, systems of linear equations, and vectors, matrices, and tensors. Maxima produces high-precision results by using exact fractions and arbitrarily long floating point representations, and can plot functions and data in two and three dimensions, while also supporting gnuplot; see www.gnuplot.info and Racine (2006) for more information regarding this powerful portable interactive data and function plotting utility. In this brief review, we describe the Maxima computer algebra system via a set of examples, and also briefly discuss some additional features that make using Maxima a joy for economists and econometricians alike. For what follows, we employ version 5.10, which was released in the fall of 2006.