cartan-core

Core trait definitions for Riemannian geometry.

This crate defines the foundational traits that all cartan manifolds, optimizers, and tools depend on. It has minimal dependencies (only rand for the Rng trait bound) and can be used standalone by downstream crates that want to implement custom manifolds against the cartan trait system.

Trait hierarchy

Manifold (base: exp, log, inner, project, validate)
  |
  +-- Retraction (cheaper exp approximation)
  +-- ParallelTransport -> VectorTransport (blanket impl)
  +-- Connection (Riemannian Hessian)
  |     |
  |     +-- Curvature (Riemann tensor, Ricci, scalar)
  +-- GeodesicInterpolation (gamma(t) sampling)

The Real type alias

All floating-point computation uses Real, currently aliased to f64. This exists so that a future version can generify over T: Scalar with a mechanical find-and-replace refactor.