实三维Clifford代数中多向量的对数
Logarithm of multivector in real 3D Clifford algebras
AI总结：
本文提出实三维Clifford代数中一般多向量对数的闭式表达式，涵盖所有p+q=3情形，并给出单刀片及组合的通用与特殊公式。
摘要：
本文给出了实几何代数Cl(p,q)中一般多向量(MV)的无基形式对数的闭式表达式，覆盖所有n=p+q=3的情况。与复数（同构于Cl(0,1)）的对数不同，由于出现两个双角反正切函数，三维对数函数允许包含由离散系数表征的两组叶面。文中提供了单个刀片及其组合的通用和特殊情形的公式。
英文摘要：
Closed form expressions for a logarithm of general multivector (MV) in base-free form in real geometric algebras (GAs) Cl(p,q) are presented for all n=p+q=3. In contrast to logarithm of complex numbers (isomorphic to Cl(0,1), 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
