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Normalization, square roots, and the exponential and logarithmic maps in geometric algebras of less than 6D.
- Source :
-
Mathematical Methods in the Applied Sciences . Feb2024, Vol. 47 Issue 3, p1425-1441. 17p. - Publication Year :
- 2024
-
Abstract
- Geometric algebras of dimension n<6$$ n<6 $$ 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 dimension n<6$$ n<6 $$ and gives efficient numerical implementations in the most popular algebras ℝ4,ℝ3,1,ℝ3,0,1$$ {\mathbb{R}}_4,{\mathbb{R}}_{3,1},{\mathbb{R}}_{3,0,1} $$, and ℝ4,1$$ {\mathbb{R}}_{4,1} $$, in the hopes of lowering the threshold for adoption of geometric algebra solutions by code maintainers. [ABSTRACT FROM AUTHOR]
- Subjects :
- *ALGEBRA
*SQUARE root
*LIE groups
Subjects
Details
- Language :
- English
- ISSN :
- 01704214
- Volume :
- 47
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Mathematical Methods in the Applied Sciences
- Publication Type :
- Academic Journal
- Accession number :
- 174780785
- Full Text :
- https://doi.org/10.1002/mma.8639