clifford: Geometric Algebra for Python

clifford is a numerical Geometric Algebra (a.k.a. Clifford algebra) package for python.

• Documentation: http://clifford.readthedocs.org
• Source code: https://github.com/pygae/clifford
• Bug reports: https://github.com/pygae/clifford/issues

Geometric Algebra (GA) is a universal algebra which among several other independent mathematical systems, subsumes:

• Complex numbers
• Quaternions
• Linear algebra

Scalars, vectors, and higher-grade entities can be mixed freely and consistently in the form of mixed-grade multivectors. Like this,

Quick Installation

Requires Python version >=3.5

Install using conda:

conda install clifford -c conda-forge

Install using pip:

pip3 install clifford

Detailed instructions

Quickstart

Try out a notebook in binder

Or have a go on your own pc:

from clifford.g3 import *  # import GA for 3D space
from math import e, pi
a = e1 + 2*e2 + 3*e3 # vector 
R = e**(pi/4*e12)    # rotor 
R*a*~R    # rotate the vector  

Syntax Summary

For installation instructions, api documention, and tutorials, head over to our documentation!

Citing This Library

As linked at the top of this page, clifford is published to zenodo. DOI 10.5281/zenodo.1453978 refers to all versions of clifford.

To obtain BibTex citation information for a specific release (recommended):

• Run python -m pip show clifford to determine which version you are using (or print clifford.__version__ from python)
• Click on the corresponding version from this list of versions
• Scroll down to the bottom of the page, and click the "BibTex" link in the "Export" sidebar

If you want to cite all releases, use:

@software{python_clifford,
  author       = {Hugo Hadfield and
                  Eric Wieser and
                  Alex Arsenovic and
                  Robert Kern and
                  {The Pygae Team}},
  title        = {pygae/clifford},
  publisher    = {Zenodo},
  doi          = {10.5281/zenodo.1453978},
  url          = {https://doi.org/10.5281/zenodo.1453978}
}