In the present paper a model of transformations of polynomial equations (the so called " direct image " model) is studied. We express, in this model, some minimal polynomials and some resolvents relative to the Galois group of a polynomial in order to use a general algorithm of resolution. This algorithm can be effectively computed in MACSYMA with the extension SYM that manipulates symmetric polynomials. We give a few examples obtained by specializing the general algorithm for the Galois resolvent.