Reconstructing Rational Functions with $\text{FireFly}$

Abstract

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

Comments: 46 pages, 3 figures, 6 tables; v2: matches published version