Logarithm of multivector in real 3D Clifford algebras
Articles
Artūras Acus
Vilnius University
Adolfas Dargys
Semiconductor Physics Institute
Published 2023-11-07
https://doi.org/10.15388/namc.2024.29.33535
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Keywords

Clifford (geometric) algebra
multivector logarithm
computer-aided theory

How to Cite

Acus, A. and Dargys, A. (2023) “Logarithm of multivector in real 3D Clifford algebras”, Nonlinear Analysis: Modelling and Control, 29(1), pp. 13–31. doi:10.15388/namc.2024.29.33535.

Abstract

Closed form expressions for a logarithm of general multivector (MV) in basis-free form in real geometric algebras (GAs) Clp,q are presented for all n = p + q = 3. In contrast to logarithm of complex numbers (isomorphic to Cl0,1), 3D logarithmic functions, due to appearance of two double angle arc tangent functions, allow to include two sets of sheets characterized by discrete coefficients. Formulas for generic and special cases of individual blades and their combinations are provided.

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