vee

Vector Expression Emitter (VEE): Geometric Algebra Code Generator

The goal of this crate is to generate optimized code for geometric algebra flavors.

Features

• Zero non-optional dependencies.
• Uniquely reduce symbolic multivector expressions for algebraic and structural equivalence to coincide.
• Generate text form in Unicode/ASCII/LaTeX mode.
• Generate code form in generic/Rust mode.
• Generate list form (i.e., s-expressions, Scheme, or egglog) in Unicode/ASCII mode.
• Generate tree form (i.e., DOT graphs as in text/vnd.graphviz) in Unicode/ASCII mode.
• Eliminate orthonormalization conditions from expressions using reflection/projection operator by factoring pinned symbols, GCD coefficients, and predominant signs.
• Evaluate symbols as rationals.
• Count operations (i.e., multiplications and additions).
• Define the metric-agnostic basis, i.e., elliptic, hyperbolic, and parabolic (Euclidean) along with the multivector entities for dimensions D = N + 1 <= 8 of the plane-based pistachio flavor, i.e., projective geometric algebra (PGA).

Roadmap

• Simplify emitter by flattening expression tree into token stream and perform defer logic during stream iteration rather than tree traversal.
• Explore egglog to further optimize expressions to reduce operation count by domain-specific common subexpression elimination (CSE) targeting exterior products. Reduce search space by leveraging applicable geometric decomposition, e.g., Euclidean decomposition for parabolic reflection operator. If promising, import expressions back.
• Generate expressions in SIMD mode.
• Define other geometric algebra flavors.

See the release history to keep track of the development.

Pseudo-Local Documentation Builds

Build the documentation with cargo-tex. Note that navigating the documentation requires web access as KaTeX is embedded via remote CDN.

cargo tex --open

License

Copyright © 2025-2026 Rouven Spreckels rs@qu1x.dev

Licensed under the terms of the MPL-2.0.

Contribution

Unless you explicitly state otherwise, any Contribution intentionally submitted for inclusion in the Covered Software by You shall be licensed as above, without any additional terms or conditions.