Geonum – geometric number library for unlimited dimensions with O(1) complexity
5 months ago
- #computational efficiency
- #geometric algebra
- #mathematical foundations
- The text critiques traditional scalar-based mathematical approaches for discarding geometric information, leading to complex and inefficient computations.
- Introduces 'geonum' as a geometric number specification that simplifies computations by preserving angle and length, reducing complexity from O(n^k) to O(1).
- Geonum uses a structure with length and angle (including blade and value) to represent numbers, enabling dimension-free geometric operations.
- Demonstrates how geonum outperforms traditional methods in speed and storage, especially in high-dimensional spaces, with constant-time operations.
- Provides practical examples and benchmarks showing geonum's efficiency, such as computing projections and rotations without predefined dimensions.
- Highlights the unification of mathematical foundations (set theory, category theory, algebraic structures) under geonum's geometric approach.
- Offers installation and usage instructions for the geonum library, including how to run tests and benchmarks.