Ecosystem Integration Design

Dependency Direction

The integration packages sit above the core autodiff layers:

autodiff/core       -> luna-generic only
autodiff/dual       -> luna-generic, arithmetic
autodiff/elementary -> arithmetic
autodiff/checked    -> arithmetic
autodiff/forward    -> core/dual/elementary
autodiff/linalg     -> autodiff + linear-algebra
autodiff/poly       -> autodiff + luna-poly

Lower-level packages do not import linear-algebra, luna-poly, floating, or type_theory.

Linear Algebra

Dual[T] is a valid scalar for ring-level vector and matrix operations because it implements the relevant Luna Flow algebraic traits when T does. The integration intentionally avoids algorithms that require Field, total division, inverses, or total ordering.

Gradients and Jacobians use n-pass forward-mode seeding. This is simple, correct, and keeps the API small. Vector-valued tangent storage is future work.

Polynomial Evaluation

The polynomial bridge reuses luna-poly data structures. It lifts coefficients to constants in Dual[T], evaluates through the existing Luna Poly algorithm, and reads the tangent as the derivative at the point.

This is automatic differentiation through evaluation, not symbolic differentiation.