A Maple package to deal with the birationality of curves and surfaces parametrizations

Abstract

In this paper we present the Maple package Luroth for dealing with the birationality of curves and surfaces parametrizations. The procedures in the package decide whether a given, either curve or surface, parametrization is injective by computing its degree map. In addition, if the parametrization is not injective, it determines a birational reparametrization. For the curve case, the corresponding command always provides an optional answer. For the surface case, not all cases are covered. Nevertheless, we illustrate using Maple some new ideas on how to approach those surface cases not covered in the package.