An interpretation of d'Inverno algorithm for Petrov classification

The purpose of this paper is to give an easy interpretation of the d'Inverno and Russel-Clark algorithm for the determination of Petrov type of general relativistic space-times starting from a quartic equation. It is shown that Petrov classification is directly connected to the zeros of the resolvent of a thirth and fourth degree equations. Petrov type may be deduced from the values of the roots of a third or second order equation.