Rationalizing roots: an algorithmic approach

Abstract

In the computation of Feynman integrals which evaluate to multiple polylogarithms one encounters quite often square roots. To express the Feynman integral in terms of multiple polylogarithms, one seeks a transformation of variables, which rationalizes the square roots. In this paper, we give an algorithm for rationalizing roots. The algorithm is applicable whenever the algebraic hypersurface associated with the root has a point of multiplicity $(d-1)$, where $d$ is the degree of the algebraic hypersurface. We show that one can use the algorithm iteratively to rationalize multiple roots simultaneously. Several examples from high energy physics are discussed.