clifford: Geometric Algebra for Python

In [1]: from clifford.g3 import *  # import GA for 3D space

In [2]: from numpy import e,pi

In [3]: a = e1 + 2*e2 + 3*e3 # vector

In [4]: R = e**(pi/4*e12)    # rotor

In [5]: R*a*~R    # rotate the vector
Out[5]: (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.

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Docs

• Tutorials
  • Installation
  • Quick Start (G2)
  • The Algebra Of Space (G3)
  • Rotations in Space: Euler Angles, Matrices, and Quaternions
  • Conformal Geometric Algebra
  • Object Oriented CGA
  • Space Time Algebra
  • Interfacing Other Mathematical Systems
  • Predefined Geometric Algebras
  • Writing high(ish) performance code with Clifford and Numba via Numpy
  • Example 1 Interpolating Conformal Objects
  • Example 2 Clustering Geometric Objects

• API
  • clifford (clifford)
  • cga (clifford.cga)
  • tools (clifford.tools)
  • Issues
  • ChangeLog

Slide Decks

• Installing

• Conformal Geometric Algeba with Python, Part 1

• Conformal Geometric Algeba with Python, Part 2

Videos

• Intro to Clifford

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Links

• Symbolic geometric algebra module for python: https://github.com/brombo/galgebra

• Cambridge GA group: http://www.mrao.cam.ac.uk/~clifford

• David Hestenes’ (The man) website: http://geocalc.clas.asu.edu/

• GAOnline - Conformal Geometric Algebra visualiser: http://gaonline.azurewebsites.net/

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