# galixir v0.28.0 - Table of Contents

> Elixir Macros implementing Geometric Algebras

## Modules

- [Galixir](Galixir.md): Galixir is a library for working with [Geometric Algebra (GA)](https://bivector.net) in Elixir.
- [Galixir.Algebras.CGA2](Galixir.Algebras.CGA2.md): Two-dimensional Conformal Geometric Algebra (CGA).
- [Galixir.Algebras.CGA3](Galixir.Algebras.CGA3.md): Three-dimensional Conformal Geometric Algebra (CGA).
- [Galixir.Algebras.Complex1](Galixir.Algebras.Complex1.md): Complex numbers represented as a one-dimensional geometric algebra.
- [Galixir.Algebras.Dual1](Galixir.Algebras.Dual1.md): Dual numbers represented as a one-dimensional degenerate geometric algebra.
- [Galixir.Algebras.Hyper1](Galixir.Algebras.Hyper1.md): Hyperbolic numbers represented as a one-dimensional geometric algebra.
- [Galixir.Algebras.PGA2](Galixir.Algebras.PGA2.md): 
This module implements two-dimensional Euclidean geometry using the
projective geometric algebra (PGA) model.
- [Galixir.Algebras.PGA3](Galixir.Algebras.PGA3.md): This module implements three-dimensional Euclidean geometry using the
projective geometric algebra (PGA) model.
- [Galixir.Algebras.Vector2](Galixir.Algebras.Vector2.md): Two-dimensional Euclidean geometric algebra, `Cl(2, 0)`.
- [Galixir.Algebras.Vector3](Galixir.Algebras.Vector3.md): Three-dimensional Euclidean geometric algebra, `Cl(3, 0)`.
- [Galixir.Blade](Galixir.Blade.md): Provides operations on basis blades using bitmask encoding.
- [Galixir.Chain](Galixir.Chain.md): Builds quoted boolean expressions from lists of quoted conditions.

- [Galixir.Generator](Galixir.Generator.md): Provides compile-time helpers for generating geometric algebra modules.
- [Galixir.Generator.BasisNames](Galixir.Generator.BasisNames.md): Generates functions that map basis-blade masks to their canonical names.

- [Galixir.Generator.Canonical](Galixir.Generator.Canonical.md): Generates helpers for determining canonical properties of multivectors.
- [Galixir.Generator.Cofficients](Galixir.Generator.Cofficients.md): Generates coefficient access functions for multivectors.
- [Galixir.Generator.Dual](Galixir.Generator.Dual.md): Generates dual and undual operations for multivectors.

- [Galixir.Generator.GeometricProduct](Galixir.Generator.GeometricProduct.md): Generates metric-aware geometric product functions for multivectors.

- [Galixir.Generator.Grade](Galixir.Generator.Grade.md): Generates functions for extracting, enumerating, and testing multivector grades.

- [Galixir.Generator.Header](Galixir.Generator.Header.md): Generates the static header implementation for a Galixir algebra module.
- [Galixir.Generator.InnerProduct](Galixir.Generator.InnerProduct.md): Generates inner, left-contraction, and right-contraction product functions.

- [Galixir.Generator.Inspect](Galixir.Generator.Inspect.md): Generates the string and `Inspect` representations of multivectors.

- [Galixir.Generator.Inverse](Galixir.Generator.Inverse.md): Generates inverse operations based on multivector reversion.

- [Galixir.Generator.LinearOps](Galixir.Generator.LinearOps.md): Generates component-wise addition, subtraction, and scaling operations.

- [Galixir.Generator.New](Galixir.Generator.New.md): Generates constructors for multivectors.

- [Galixir.Generator.Norm](Galixir.Generator.Norm.md): Generates multivector norm, normalization, and canonicalization functions.

- [Galixir.Generator.Predicates](Galixir.Generator.Predicates.md): Generates predicates and guards for multivector properties.

- [Galixir.Generator.Reverse](Galixir.Generator.Reverse.md): Generates reversion operations for multivectors.

- [Galixir.Generator.ScalarProduct](Galixir.Generator.ScalarProduct.md): Generates scalar-product functions for multivectors.

- [Galixir.Generator.Sigil](Galixir.Generator.Sigil.md): Generates the `~G` sigil for constructing multivectors from strings.

- [Galixir.Generator.Utils](Galixir.Generator.Utils.md): Provides shared AST and documentation helpers for algebra generators.

- [Galixir.Generator.WedgeProduct](Galixir.Generator.WedgeProduct.md): Generates outer (wedge) product functions for multivectors.

- [Galixir.GeneratorBehaviour](Galixir.GeneratorBehaviour.md): Defines the behaviour contract for Galixir code generators.
- [Galixir.GeneratorRegistry](Galixir.GeneratorRegistry.md): Provides the registry of code generators used to build Galixir algebra modules.
- [Galixir.GeometricAlgebra](Galixir.GeometricAlgebra.md): Provides a macro for generating concrete geometric algebra modules.
- [Galixir.Meta](Galixir.Meta.md): Stores the compile-time metadata used to generate a geometric algebra module.

- [Galixir.Table](Galixir.Table.md): Provides utilities for generating geometric product lookup tables.

