J.H. Davenport
Galois Groups and the Simplification of Polynomials
Cet article décrit des interfaces entre la théorie des groupes
de Galois et la facturation des polynomes.
It is well-known that the theory of Galois groups is closely
connected to the factorization of polynomials, but in practice
the connection is not as strong as one would like. There are
three areas in which one could wish for better interfaces than
one currently has. Polynomial factorization does not make much
use of Galois theory at the moment. Computational Galois Theory
tends to restrict its attention to transitive groups, whereas
some of the more interesting observations about polynomial sim
plification come from non-transitive groups. Computational Galois
Theory tends to regard polynomial factorization as a solved ques
tion, whose results can be relied on in the determination of Ga
lois groups, whereas in fact some of the polynomials that need to
be factored are distinctly non-trivial.