Resolvents and symmetric functions

摘要

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.