Algorithmic computation of multivector inverses and characteristic polynomials in non-degenerate Clifford algebras

2023/08/04 by Dimiter Prodanov, Prodanov, Dimiter
Mathematics · #15A66 #Algebraic and Geometric Analysis #FOS: Computer and information sciences #FOS: Mathematics #Numerical Analysis (math.NA) #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.2308.02291

openalex publication_date 2023/08/04 · openalex created_date 2023/08/08 · openalex updated_date 2026/07/28

Abstract

The power of Clifford or, geometric, algebra lies in its ability to represent geometric operations in a concise and elegant manner. Clifford algebras provide the natural generalizations of complex, dual numbers and quaternions into non-commutative multivectors. The paper demonstrates an algorithm for the computation of inverses of such numbers in a non-degenerate Clifford algebra of an arbitrary dimension. The algorithm is a variation of the Faddeev-LeVerrier-Souriau algorithm and is implemented in the open-source Computer Algebra System Maxima. Symbolic and numerical examples in different Clifford algebras are presented.

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