## Journal of Geometry and Symmetry in Physics

- J. Geom. Symmetry Phys.
- Volume 43 (2017), 73-105.

### 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.

#### Article information

**Source**

J. Geom. Symmetry Phys., Volume 43 (2017), 73-105.

**Dates**

First available in Project Euclid: 12 May 2017

**Permanent link to this document**

https://projecteuclid.org/euclid.jgsp/1494605781

**Digital Object Identifier**

doi:10.7546/jgsp-43-2017-73-105

**Zentralblatt MATH identifier**

1372.65129

**Subjects**

Primary: 08A70: Applications of universal algebra in computer science

Secondary: 11E88: Quadratic spaces; Clifford algebras [See also 15A63, 15A66] 15A69: Multilinear algebra, tensor products 15A75: Exterior algebra, Grassmann algebras 94B27: Geometric methods (including applications of algebraic geometry) [See also 11T71, 14G50]

**Keywords**

Clifford product computer algebra Dirac operator electromagnetism geometric product multilinear algebra outer product vector derivative

#### Citation

Prodanov, Dimiter. Clifford Algebra Implementations in Maxima. J. Geom. Symmetry Phys. 43 (2017), 73--105. doi:10.7546/jgsp-43-2017-73-105. https://projecteuclid.org/euclid.jgsp/1494605781