cartan-core 0.8.1

Core traits for Riemannian geometry and fiber bundles: Manifold, Fiber, DiscreteConnection, ParallelTransport, Curvature, GA rotors
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# cartan-core

Core trait definitions for Riemannian geometry.

[![crates.io](https://img.shields.io/crates/v/cartan-core.svg)](https://crates.io/crates/cartan-core)
[![docs.rs](https://docs.rs/cartan-core/badge.svg)](https://docs.rs/cartan-core)

Part of the [cartan](https://crates.io/crates/cartan) workspace.

## Overview

`cartan-core` defines the foundational trait hierarchy that all cartan
manifolds, optimizers, and geometric tools depend on. It has minimal
dependencies (only `rand` for RNG trait bounds) and can be used standalone
by downstream crates that implement custom manifolds against the cartan
trait system.

The trait hierarchy is:

```text
Manifold (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)
```

All floating-point computation uses the `Real` type alias (currently `f64`),
so that a future generic refactor is mechanical. The crate also provides
`CartanError` for structured error handling across the workspace.

## Fiber bundles and rotors

`cartan-core` also defines associated fiber bundles over simplicial meshes:
the `Fiber` trait (with `U1Spin2`, `TangentFiber`, `NematicFiber3D`), discrete
connections (`DiscreteConnection`, `EdgeTransport2D/3D`), and the covariant
Laplacian `CovLaplacian`. Parallel transport can be carried either as SO(d)
matrices or as geometric-algebra rotors (`Rotor2`, `Rotor3`, `RotorConnection`,
`CovLaplacian::apply_rotor`): a rotor stores the same rotation in fewer floats,
composes cheaply, and reverses by conjugation. The matrix and rotor paths agree
to floating-point tolerance, so either can be used interchangeably.

## Example

```rust,no_run
use cartan_core::{Manifold, Real};

/// Check that a point lies on the manifold and compute a tangent norm.
fn tangent_norm<M: Manifold>(m: &M, p: &M::Point, v: &M::Tangent) -> Real {
    assert!(m.check(p).is_ok());
    m.inner(p, v, v).sqrt()
}
```

## no_std

Disable default features and enable `alloc` for embedded targets:

```toml
cartan-core = { version = "0.8", default-features = false, features = ["alloc"] }
```

## License

[MIT](LICENSE-MIT)