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Sparse representations of Clifford and tensor algebras in maxima. (English) Zbl 1367.15040

Summary: 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.

MSC:

15A66 Clifford algebras, spinors
15A69 Multilinear algebra, tensor calculus
78A25 Electromagnetic theory (general)
78M25 Numerical methods in optics (MSC2010)
11E88 Quadratic spaces; Clifford algebras
94B27 Geometric methods (including applications of algebraic geometry) applied to coding theory
53A45 Differential geometric aspects in vector and tensor analysis
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References:

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