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

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Requires Python version >=3.5

Install using conda:

conda install clifford -c conda-forge

Install using pip:

pip3 install clifford

Detailed instructions

Quickstart

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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 + 2e2 + 3e3 # vector  R = e*(pi/4e12)    # rotor  Ra~R    # rotate the vector

Syntax Summary

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| Syntax | Operation | |:-:|:-:| | \| | Symmetric inner product | | << | Left contraction | | ^ | Outer product | | * | Geometric product | | X\(i\) | Return the section of the multivector X of grade i | | X\(ei\) | Return the section of the multivector X for which ei is the pseudo scalar | | X\[i\] | Return the i'th coefficient from the multivector X | X.normal() | Return the normalised multivector so that X*~X is +- 1 |

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

Citing This Library

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For citation information, see our CITATION.md file.