Journal of Geometry and Symmetry in Physics

Clifford Algebra Implementations in Maxima

Dimiter Prodanov

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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

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

First available in Project Euclid: 12 May 2017

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Zentralblatt MATH identifier

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]

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


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

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