https://github.com/jlaragonvera/Geometric-Algebra

Mathematica packages for geometric algebra
https://github.com/jlaragonvera/Geometric-Algebra

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Mathematica packages for geometric algebra

• Host: GitHub
• URL: https://github.com/jlaragonvera/Geometric-Algebra
• Owner: jlaragonvera
• License: bsd-3-clause
• Created: 2017-11-03T23:03:54.000Z (about 7 years ago)
• Default Branch: master
• Last Pushed: 2023-10-23T18:36:24.000Z (about 1 year ago)
• Last Synced: 2024-08-20T03:32:05.243Z (4 months ago)
• Language: Mathematica
• Size: 342 KB
• Stars: 42
• Watchers: 10
• Forks: 13
• Open Issues: 0
• Metadata Files:
  • Readme: README.md
  • License: LICENSE

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README

        
# Geometric Algebra

*Mathematica* packages for Clifford (geometric) algebra calculations:

## CGAlgebra 

**CGAlgebra.m** is a *Mathematica* package for the 5D Conformal Geometric Algebra.

This package contains declarations for calculations with Conformal

Geometric Algebra. Basis vectors {e0, e1, e2, e3, eInfinity} are 

denoted by e[0], e[1], e[2], e[3], e[Infinity]. Geometric products

of basis elements are denoted as e\[0,1,2\] (= e0 e1 e2), etc.

   

The results of any calculation is given in terms of the geometric product

of basis elements, that is, the outer (Grassman) product of basis

elements or multivectors is calculated by using OuterProduct[] and the

output is given in terms of geometric product of basis vectors.

        

Examples:

The vector e0 + 2 e1 + eInfinity is written as:

              

         A = e[0] + 2 e[1] + e[\[Infinity]];

         

The multivector a + 5 e1 +  e1e2e3 is

              

         B = a + 5 e[1] + e[1,2,3];

The geometric product

        GeometricProduct[A,B]

yields:

     10 + a e[0] + 2a e[1] + a e[\[Infinity]] + 5 e[0,1] - 5 e[1,\[Infinity]] + 2 e[2,3] + e[0,1,2,3] - e[1,2,3,\[Infinity]]

The inner product

       InnerProduct[A,B]

yields

       10 + 2 e[2,3]

A tutorial can be downloaded from:

## Clifford

**clifford.m** is the most recent version of the package by G. Aragon-Camarasa, G. Aragon-Gonzalez, J.L. Aragon and M.A. Rodriguez-Andrade. A user guide (**CliffordUserGuide**) is available, as well as *Mathematica* palette (**CliffordPalette**). The fundamentals of the package are presented in:

## CliffordBasic

**CliffordBasic.m** is a completely renewed but reduced version of **clifford.m** package by G. Aragon-Camarasa, G. Aragon-Gonzalez, J.L. Aragon and M.A. Rodriguez-Andrade:

Using rule-base programming the algebra over Rp,q in arbitrary dimensions is constructed as in A. Macdonald "An Elementary Construction of Geometric Algebra", Adv. Appl. Cliff. Alg. 12 (2002) 1-6.

In **CliffordBasic**, the j-th basis vector is denoted by e[j] and the geometric product of basis vectors, such as e1e3e4, as `e[1,3,4]`.

Examples:     

The vector e1 + 2 e2 - a e3 is written as   

      

        A = e[2] + 2 e[2] - a e[3];

                  

The The multivector a + 5 e1 + e1 e2 e3 is written as           

              

         B = a + 5 e[1] + e[1,2,3];

         

The geometric product AB is calculated as 

        GeometricProduct[A,B]

yielding:

        3 a e[2] - a^2 e[3] - 15 e[1,2] - a e[1,2] - 3 e[1,3] + 5 a e[1,3]

    

which can be factored using

         GFactor[%]

         

         3 a e[2] - a^2 e[3] + (-15-a) e[1,2] + (-3 + 5 a)e[1,3]

         

The signature of the Rp,q is set by `$SetSignature={p,q}`. If not specified,

the default value is:

         $SetSignature={20,0}