Interpolation of Dense and Sparse Rational Functions and other Improvements in $\text{FireFly}$

Abstract

We present the main improvements and new features in version $\text{2.0}$ of the open-source $\text{C++}$ library $\text{FireFly}$ for the interpolation of rational functions. This includes algorithmic improvements, e.g. a hybrid algorithm for dense and sparse rational functions and an algorithm to identify and remove univariate factors. The new version is applied to a Feynman-integral reduction to showcase the runtime improvements achieved. Moreover, $\text{FireFly}$ now supports parallelization with $\text{MPI}$ and offers new tools like a parser for expressions or an executable for the insertion of replacement tables.

Comments: 28 pages, 10 tables, 1 figure