Reconstructing Rational Functions with $\texttt{FireFly}$

TL;DR

The paper introduces FireFly, an open-source C++ library for reconstructing multivariate rational functions over finite fields, demonstrating its application in integration-by-parts reductions and comparing its efficiency to existing algebraic methods.

Contribution

The paper presents FireFly, a new open-source library with algorithms for rational function reconstruction, and evaluates its performance in practical computational physics tasks.

Findings

FireFly efficiently reconstructs rational functions over finite fields.

FireFly outperforms algebraic approaches in runtime and memory in IBP reductions.

The library is openly available for scientific use.

Abstract

We present the open-source $\texttt{C++}$ library $\texttt{FireFly}$ for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use $\texttt{FireFly}$ in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program $\texttt{Kira}$.