A simple and efficient algorithm for computing the Baker-Campbell-Hausdorff series

TL;DR

This paper introduces a straightforward, efficient algorithm for computing the Baker-Campbell-Hausdorff series coefficients, optimized for implementation in various programming environments, emphasizing integer arithmetic for speed.

Contribution

The paper presents a novel algorithm that simplifies and accelerates the computation of BCH series coefficients using integer arithmetic, suitable for general-purpose programming languages.

Findings

Algorithm avoids rational arithmetic, enhancing efficiency.

Implementation in Julia demonstrates practical applicability.

Computes BCH coefficients straightforwardly and efficiently.

Abstract

A new algorithm for computing coefficients of the Baker--Campbell--Hausdorff series is presented, which can be straightforwardly implemented in any general-purpose programming language or computer algebra system. The algorithm avoids rational arithmetic and performs all its calculations in pure integer arithmetic, allowing for a very efficient implementation. An implementation in the Julia programming language is available.