Reconstructing rational functions with FireFly

We present the open-source C++ library FireFly for the reconstruction of multivariate rational functions over finite fields. We discuss the involved algorithms and their implementation. As an application, we use FireFly in the context of integration-by-parts reductions and compare runtime and memory consumption to a fully algebraic approach with the program Kira. Program summary Program title: FireFly Program files doi: http://dx.doi.org/10.17632/nzgxdwwt8k.1 Licensing provisions: GNU General Public License 3 Programming language: C++ External routines/libraries used: GNU GMP [1], FLINT[2] Nature of problem: The interpolation of an unknown rational function, called black box, from only its evaluations can be used in many physical contexts where algebraic calculations fail due to memory and time restrictions. Solution method: The black-box function is evaluated at different points over a finite field. These points are then used by interpolation algorithms [3,4] to obtain the analytic form of the black-box function. The members of a finite field are promoted to Q using a rational reconstruction algorithm [5,6]. Restrictions: The CPU time and the available RAM (C) 2019 Elsevier B.V. All rights reserved.