Galois ideals and groups
Quaderni Elettronici del Seminario di Geometria Combinatoria 22E 1--39
Dipartimento di Matematica,
Università degli Studi di Roma "La Sapienza", Italie.
Note. Transparents de la conférence du 22 Avril 2004
Ideali di Galois in teoria di Galois computazionale
présentée au Seminario di
Geometria Combinatoria "Giuseppe Tallini" .
Abstract.
We present various methods for determining the Galois ideal of a
univariate polynomial f(x). The Galois ideal is the ideal of
the relations with coefficients in the base field satified by the roots of
f(x). These methods make use of:
- the Galois resolvent;
- the G-resolvent (where G is the Galois group of
f(x));
- factorizations in extensions.
Advantages and inconvenients of each method are discussed.