Reconstruction of rational functions made simple

TL;DR

This paper introduces a novel method for reconstructing rational functions using finite-field sampling, which reduces sample requirements and improves efficiency, especially in Feynman integrals reduction for particle physics.

Contribution

The paper presents a new approach that exploits linear relations among functions to efficiently reconstruct rational functions with fewer samples.

Findings

Significantly reduces the number of samples needed for reconstruction

Improves computational efficiency in Feynman integrals reduction

Demonstrates effectiveness on particle physics examples

Abstract

We present a new method for the reconstruction of rational functions through finite-fields sampling that can significantly reduce the number of samples required. The method works by exploiting all the independent linear relations among target functions. Subsequently, the explicit solutions of the functions can be efficiently obtained by solving the linear system. As a first application, we utilize the method to address various examples within the context of Feynman integrals reduction. These examples demonstrate that our method can substantially improve the computational efficiency, making it useful for future computations in particle physics.