Galixir

Geometric Algebra implementation in Elixir.

Generate a concrete algebra with Galixir.GeometricAlgebra:

defmodule Example.PGA3 do
  use Galixir.GeometricAlgebra,
    metric: {1, 1, 1, 0},
    bases: {"1", "2", "3", "0"}
end

The package already provides Galixir.Algebras.PGA3, which adds point, motor, and geometry helpers to the generated operations. For example, align two pairs of corresponding points and transform a third point:

alias Galixir.Algebras.PGA3

from = [PGA3.point(0, 0, 0), PGA3.point(1, 0, 0)]
to = [PGA3.point(0, 0, 0), PGA3.point(0, 1, 0)]
motor = PGA3.align(from, to)

PGA3.point(1, 0, 0)
|> PGA3.transform(motor)
|> PGA3.point_coordinates()
# => {0.0, 1.0, 0.0}

Installation

def deps do
  [
    {:galixir, "~> 0.34.0"}
  ]
end

The package includes projective (PGA2, PGA3, PGA4), conformal (CGA2, CGA3), and Euclidean vector (Vector2, Vector3) algebras. The generated core provides multivector operations; the concrete modules offer different sets of higher-level geometry helpers. Complex1 represents complex numbers as a geometric algebra. See the introduction for where to start.

Contributions are welcome. See Contributing for setup, validation commands, numerical conventions, and release checks.

Licensed under the Apache License 2.0. The full license text is included in LICENSE.

Example

This Livebook uses 3D projective geometric algebra (PGA3) to render a scene as SVG. Open it in Livebook to use the interactive camera controls.

3D Projective Geometric Algebra

2D Conformal Geometric Algebra