Alice

A rigorous topology and algebra library from first principles, with Lie group machinery.

on crates.io as alice-math. Import as alice via the package alias

[dependencies]
alice = { package = "alice-math", version = "0.1.0" }

What it is

Alice builds the mathematical foundations needed for Lie group simulation and Riemannian optimizationfrom the ground up in Rust. The algebraic hierarchy starts at Magma and builds to Field. The topology layer encodes open set axioms, manifolds, and smooth structure. The groups module provides concrete matrix Lie groups with correct constraint enforcement and no_std compatibility.

Modules

alice::core — Algebraic hierarchy (Magma through Field), FiniteF64, Rational, morphisms
alice::topology — Topological spaces, manifolds, smooth structure, metric spaces
alice::algebra — Lie algebras, Lie bracket, Baker-Campbell-Hausdorff formula
alice::maps — Exponential and logarithmic maps via Padé approximation and eigendecomposition
alice::groups — GL, SL, SO, SE, Aff with full constraint enforcement at construction

Quick example

use alice::groups::so::So;
use alice::maps::exp_log::HasExpMap;
use alice::topology::manifold::Dynamic;

let theta = std::f64::consts::PI / 4.0;
let rotation = So::new(
    vec![theta.cos(), -theta.sin(), theta.sin(), theta.cos()],
    Dynamic::new(2),
).unwrap();

let log = rotation.log().unwrap();
let recovered = So::exp(&log);

Design

no_std + alloc compatible
Algebraic axioms enforced at the type level where possible, at construction otherwise
All group constructors return Result<Self, GroupError> rather than panicking

Companion crate

riemannian-gd provides Riemannian gradient descent over Lie groups, consuming alice-math as its foundation.

Status

0.1.0 — API is functional and tested. Atlas implementations for concrete groups, additional Lie group examples, and Manim visualizations are planned for subsequent releases.

License

MIT

alice-math 0.1.0