by Alan Bromborsky
Abstract: This document describes the implementation of a geometric algebra module in python that utilizes the sympy symbolic algebra library. The python module GA has been developed for coordinate free calculations using the operations (geometric, outer, and inner products etc.) of geometric algebra. The operations can be defined using a completely arbitrary metric defined by the inner products of a set of arbitrary vectors or the metric can be restricted to enforce orthogonality and signature constraints on the set of vectors. In addition the module includes the geometric, outer (curl) and inner (div) derivatives and the ability to define a curvilinear coordinate system. The module requires the numpy and the sympy modules.
This module is, e.g., used in the undergraduate textbooks by Alan Macdonald:
- Geometric Algebra Module for Sympy
- What is Geometric Algebra?
- Vector Basis and Metric
- Representation and Reduction of Multivector Bases
- Base Representation of Multivectors
- Blade Representation of Multivectors
- Outer and Inner Products, Left and Right Contractions
- Reverse of Multivector
- Reciprocal Frames
- Geometric Derivative
- Module Components
Source: http://docs.sympy.org/0.7.0/modules/galgebra/GA/GAsympy.html as of 04 Dec. 2013.