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Geometric algebras of dimensionn  &lt;  6   $$ n&amp;lt;6 $$    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 dimensionn  &lt;  6   $$ n&amp;lt;6 $$    and gives efficient numerical implementations in the most popular algebrasℝ    4    ,ℝ    3,1    ,ℝ    3,0  ,  1$$ {\mathbb{R}}_4,{\mathbb{R}}_{3,1},{\mathbb{R}}_{3,0,1} $$   , andℝ    4,1$$ {\mathbb{R}}_{4,1} $$   , in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers.

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