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

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.

Citation

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

Information

Published: 2017
First available in Project Euclid: 12 May 2017

zbMATH: 1372.65129
Digital Object Identifier: 10.7546/jgsp-43-2017-73-105

Subjects:
Primary: 08A70
Secondary: 11E88 , 15A69 , 15A75 , 94B27

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

Rights: Copyright © 2017 Institute of Biophysics and Biomedical Engineering, Bulgarian Academy of Sciences

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