geonum-0.2.1 has been yanked.

geonum

use

cargo add geonum

see tests/lib_test.rs examples for scalable numerical simulation of linear and geometric algebra operations

benches

rank-3 tensor comparison

implementation	size	time
tensor (O(n³))	2	1.06 µs
tensor (O(n³))	3	2.25 µs
tensor (O(n³))	4	3.90 µs
tensor (O(n³))	8	7.92 µs
tensor (O(n³))	16	69.54 µs
geonum (O(1))	any	9.83 ns

geonum achieves constant O(1) time complexity regardless of problem size, 400× faster than tensor operations at size 4 and 7000× faster at size 16, eliminating cubic scaling of traditional tensor implementations

extreme dimension comparison

implementation	dimensions	time	storage complexity
traditional ga	10	543.40 ns (partial)	O(2^n) = 1024 components
traditional ga	30	theoretical only	O(2^n) = 1 billion+ components
traditional ga	1000	impossible	O(2^{1000) ≈ 10}301 components
traditional ga	1,000,000	impossible	O(2^1000000) components
geonum (O(1))	10	134.12 ns	O(1) = 2 components
geonum (O(1))	30	153.64 ns	O(1) = 2 components
geonum (O(1))	1000	2.08 µs	O(1) = 2 components
geonum (O(1))	1,000,000	2.94 ms	O(1) = 2 components

geonum enables geometric algebra in million-dimensional spaces with constant time operations, achieving whats mathematically impossible with traditional implementations (requires more storage than atoms in the universe)

tests

cargo fmt --check # format check
cargo clippy # lint
cargo test --lib # unit
cargo test --test lib_test # feature
cargo bench # bench
cargo llvm-cov # coverage

docs

cargo doc --open

todo

dot product, wedge product, geometric product
inverse, division, normalization
million-dimension geometric algebra with O(1) complexity
multivector support and trivector operations
rotations, reflections, projections, rejections
exponential, interior product, dual operations
meet and join, commutator product, sandwich product

geonum 0.2.1