GeometricAlgebra

Mathematica package for Clifford (geometric) algebra calculations Version (2024-06-14)

Quick startup

1. Unzip the content preserving directory structure
2. Open GA.nb and follow setup & configuration instructions in the beginning of the notebook.
3. Open UsageExamples/01_Start.nb notebook and try to repeat calculations.

Main features

• Textbook notation and precedences of products (without Mathematica palettes)
• Algebraic operations in orthonormal frame (additive representation, symbolic coefficients)
• Multiple algebras in the same Mathematica session
• Matrix representations of Cl(p,q) algebras (two algorithms)
• Idempotents with different basis sorting
• Main involutions and general multivector inverse
• Algebraic (ideal) and operator (Hestenes) spinors (not finished)
• Series of elementary functions of Cl(p,q) (one MV argument functions only)
• Functions for MV (arbitrary Cl(p,q) algebras)
• Sorting/ordering of general MV
• Transformation and AdjointTranformation for linear transformations
• Clifford calculus (directional and vector derivatives) in arbitrary signature flat space

Short file description

• GA.nb (main file, contains installation information)
• UnicodeCharactersAdd.tr (add-on for Mathematica system file for Linux and Mac)
• UnicodeCharactersAddWin10.tr (add-on for Mathematica system file for Windows)