Normalization, square roots, and the exponential and logarithmic maps in geometric algebras of less than 6D

Abstract

Geometric algebras of dimension are becoming increasingly popular for the modeling of 3D and 3 + 1D geometry. With this increased popularity comes the need for efficient algorithms for common operations such as normalization, square roots, and exponential and logarithmic maps. The current work presents a signature‐agnostic analysis of these common operations in all geometric algebras of dimension and gives efficient numerical implementations in the most popular algebras , and , in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers.