Scaling up to Multivariate Rational Function Reconstruction

TL;DR

This paper introduces an efficient algorithm for reconstructing multivariate rational functions from black-box probes, significantly aiding complex calculations in high-energy physics by reducing the number of necessary evaluations.

Contribution

It presents a nearly optimal algorithm for multivariate rational function reconstruction, reducing probe counts in dense coefficient scenarios.

Findings

Algorithm is nearly optimal for dense coefficients

Reduces number of black-box probes needed

Applicable to high-energy physics amplitude calculations

Abstract

I present an algorithm for the reconstruction of multivariate rational functions from black-box probes. The arguably most important application in high-energy physics is the calculation of multi-loop and multi-leg amplitudes, where rational functions appear as coefficients in the integration-by-parts reduction to basis integrals. I show that for a dense coefficient the algorithm is nearly optimal, in the sense that the number of required probes is close to the number of unknowns.