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Advances in Applied Clifford Algebras

, Volume 27, Issue 1, pp 661–683 | Cite as

Sparse Representations of Clifford and Tensor Algebras in Maxima

  • D. Prodanov
  • V. T. Toth
Article

Abstract

Clifford algebras have broad applications in science and engineering. The use of Clifford algebras can be further promoted in these fields by availability of computational tools that automate tedious routine calculations. We offer an extensive demonstration of the applications of Clifford algebras in electromagnetism using the geometric algebra \({\mathbb{G}^3 \equiv C\ell_{3,0}}\) as a computational model in the Maxima computer algebra system. We compare the geometric algebra-based approach with conventional symbolic tensor calculations supported by Maxima, based on the itensor package. The Clifford algebra functionality of Maxima is distributed as two new packages called clifford—for basic simplification of Clifford products, outer products, scalar products and inverses; and cliffordan—for applications of geometric calculus.

Keywords

Computer algebra Geometric algebra Tensor calculus Maxwell’s equations 

Mathematics Subject Classification

Primary 08A70 11E88 Secondary 94B27 53A45 15A69 

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Copyright information

© Springer International Publishing 2016

Authors and Affiliations

  1. 1.Department of Environment, Health and SafetyNeuroscience Research Flanders, IMEC vzwLeuvenBelgium
  2. 2.Center for Research on Integrated Sensors PlatformsCarleton UniversityOttawaCanada

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