# 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.

## Key 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 $\texttt{Kira}$.

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Source: https://tomesphere.com/paper/1904.00009