Logarithm of multivector in real 3D Clifford algebras

IF 2.6 3区数学 Q1 MATHEMATICS, APPLIED

Nonlinear Analysis-Modelling and Control Pub Date : 2023-11-07 DOI:10.15388/namc.2024.29.33535

Artūras Acus, Adolfas Dargys

引用次数: 1

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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真实三维Clifford代数中多向量的对数

在实几何代数(GAs) Clp,q中，对于所有n = p + q = 3，给出了无基形式的一般多向量(MV)的对数的封闭表达式。与复数的对数(同构于Cl0,1)相反，三维对数函数由于两个双角弧切函数的出现，允许包含两组以离散系数为特征的片。给出了单个叶片及其组合的一般和特殊情况的公式。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Nonlinear Analysis-Modelling and Control MATHEMATICS, APPLIED-MATHEMATICS, INTERDISCIPLINARY APPLICATIONS

CiteScore

3.80

自引率

10.00%

发文量

审稿时长

9.6 months

期刊介绍： The scope of the journal is to provide a multidisciplinary forum for scientists, researchers and engineers involved in research and design of nonlinear processes and phenomena, including the nonlinear modelling of phenomena of the nature. The journal accepts contributions on nonlinear phenomena and processes in any field of science and technology. The aims of the journal are: to provide a presentation of theoretical results and applications; to cover research results of multidisciplinary interest; to provide fast publishing of quality papers by extensive work of editors and referees; to provide an early access to the information by presenting the complete papers on Internet.