A Succinct Multivariate Lazy Multivariate Tower AD for Weil Algebra Computation

TL;DR

This paper introduces a functional implementation of Multivariate Tower Automatic Differentiation designed for computing $C^$-structures of arbitrary Weil algebras, advancing the computational tools for differential geometry.

Contribution

It presents a novel functional implementation of multivariate tower AD specifically aimed at Weil algebra computations, extending previous theoretical work.

Findings

Efficient implementation of multivariate tower AD

Enables $C^$-structure computations for Weil algebras

Supports arbitrary Weil algebra computations

Abstract

We propose a functional implementation of \emph{Multivariate Tower Automatic Differentiation}. Our implementation is intended to be used in implementing $C^\infty$-structure computation of an arbitrary Weil algebra, which we discussed in the previous work.