RationalizeRoots: Software Package for the Rationalization of Square Roots

TL;DR

The paper presents RationalizeRoots, a software package (Mathematica and Maple) that implements Besier:2018jen's rationalization algorithm to transform square-root kernels appearing in Feynman integrals into rational functions, enabling expressions in terms of multiple polylogarithms. It provides both a general framework (through hypersurface parametrization, projective closures, and the F-Decomposition Theorem) and practical tools (ParametrizePolynomial and RationalizeRoot) to handle single and multiple square roots, including advanced strategies for simultaneous rationalization. The authors illustrate the approach with detailed examples, discuss handling of perfect-square factors, and show how the tool integrates with existing CAS workflows. The package has already informed recent perturbative calculations and offers a principled path toward broader, systematic rationalization in high-energy physics computations.

Abstract

The computation of Feynman integrals often involves square roots. One way to obtain a solution in terms of multiple polylogarithms is to rationalize these square roots by a suitable variable change. We present a program that can be used to find such transformations. After an introduction to the theoretical background, we explain in detail how to use the program in practice.