Journal of Geometry and Symmetry in Physics

Clifford Algebra Implementations in Maxima

Dimiter Prodanov

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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


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