Clifford Algebra Implementations in Maxima

Abstract

This tutorial focuses on the packages $\texttt{clifford}$ and $\texttt{cliffordan}$ for the computer algebra system Maxima. Maxima is the open source descendant of the first computer algebra system and features a rich functionality from a large number of shared packages. The Maxima language is based on the ideas of functional programming, which is particularly well suited for transformations of formal mathematical expressions. While $\texttt{clifford}$ implements Clifford algebras $C\ell_{p,q,r}$ of arbitrary signatures and order based on the elementary construction of Macdonald, $\texttt{cliffordan}$ features geometric calculus functionality. Using $\texttt{clifford}$ expressions containing geometric, outer and inner products can be simplified. Applications of $\texttt{clifford}$ and $\texttt{cliffordan}$ in linear algebra and calculus are demonstrated.