This formula is not satisfactory under a computing point of view because it introduces more algebraic quantities than necessary. The number P(a)/Q'(a) is called the residue of the root a of Q. We introduce the notion of multiplicity of a residue b that is the number of roots a having b as a residue. Trager (1976) introduced a new formula involving less algebraic numbers: let S(y) be the resultant S(y) = Resx[P(x) yQ'(x ), Q(x)-l; we have