  In this paper we consider the problem of working with rational functions in a
numeric environment. A particular problem when modeling with such functions is
the existence of Froissart doublets, where a zero is close to a pole. We
discuss three different parameters which allow one to monitor the absence of
Froissart doublets for a given general rational function. These include the
euclidean condition number of an underlying Sylvester-type matrix, a parameter
for determing coprimeness of two numerical polynomials and bounds on the
spherical derivative. We show that our parameters sharpen those found in a
previous paper by two of the autours.
