A geometric algebra Mathematica module for Euclidean 2D and 3D spaces using the Pauli basis representation as a backend, and a Mathematica module for STA (relativistic space with a +,-,-,- signature).
Four modules are provided:
- Cl20
- GA20
- GA30
- GA13
Which implement GA(2,0), GA(2,0), GA(3,0), and GA(1,3) algebras respectively. The first is implemented using pairs of complex numbers, the second with only the real Pauli matrixes (\sigma_1, and \sigma_3), the third uses all three Pauli matrices, and the last uses Dirac matrices.
Three generic test notebooks are provided, each of which also provides some documentation
- testCl20.nb Test cases and documentation for Cl20.m
- testGA20.nb Test cases and documentation for GA20.m (online (w/o Mathematica) viewable version saved as testGA20.pdf)
- testGA30.nb Test cases and documentation for GA30.m (online (w/o Mathematica) viewable version saved as testGA30.pdf)
- testGA13.nb Test cases and documentation for GA13.m (online (w/o Mathematica) viewable version saved as testGA13.pdf)
Some other ad-hoc demonstrations are also available:
- bivectorCommutatorGA13.nb -- symbolic verification that {0,4} = (1/2(AB + BA), and {2} = (1/2(AB - BA) for STA bivectors A,B.
- lorentzForce.nb -- The Force and power components of the covariant (STA) Lorentz force equation are expanded symbolically.
- shortCurrentFilament.nb -- don't remember.
- ellipticParameterization.nb -- don't remember.
- triangleInscribedCircle.nb -- This computes the center point vector and the radius for a circle inscribed in a triangle. Graphical demonstration of the solution with Animate. Uses Cl20
TODO:
-
Don't think I added tests for *ectorSelection[..., False] for all cases.
-
GA30: Added Power[_, -1]. Do the same for the other modules.
-
Added Normalize to GA20, Cl20, and GA13 -- but didn't test yet.