clifford: Geometric Algebra for Python¶
In : from clifford.g3 import * # import GA for 3D space In : from numpy import e,pi In : a = e1 + 2*e2 + 3*e3 # vector In : R = e**(pi/4*e12) # rotor In : R*a*~R # rotate the vector Out: (2.0^e1) - (1.0^e2) + (3.0^e3)
This module implements Geometric Algebras (a.k.a. Clifford algebras). Geometric Algebra (GA) is a universal algebra which subsumes complex algebra, quaternions, linear algebra and several other independent mathematical systems. Scalars, vectors, and higher-grade entities can be mixed freely and consistently in the form of mixed-grade multivectors.
If you think Geometric Algebra looks interesting and want to learn more, check out the cambridge groups page, and here are some great introductory textbooks!
- Geometric Algebra for Physicists, by Doran and Lasenby
- Geometric Algebra for Computer Science, by Dorst, Fontijne and Mann
- New Foundations for Classical Mechanics, by David Hestenes