D-resultant for rational functions

In this paper we introduce the D-resultant of two rational functions f(t), g(t) ≤ K(t) and show how it can be used to decide if K(f(t), g(t)) = K(t) or if K[t] ⊂ K[f(t),g(t)] and to find the singularities of the parametric algebraic curve define by X = f(t),Y = g(t). In the course of our work we extend a result about implicitization of polynomial parametric curves to the rational case, which has its own interest.published_or_final_versio