  The theory of p-ramification, regarding the Galois group of the maximal
pro-p-extension of a number field K, unramified outside p and $\infty$, is well
known including numerical experiments with PARI/GP programs. The case of
``incomplete p-ramification'' (i.e., when the set S of ramified places is a
strict subset of the set P of the p-places) is, on the contrary, mostly unknown
in a theoretical point of view. We give, in a first part, a way to compute, for
any S $\le$ P, the structure of the Galois group of the maximal S-ramified
abelian pro-p-extension H\_(K,S) of any field K given by means of an
irreducible polynomial. We publish PARI/GP programs usable without any special
prerequisites. Then, in an Appendix, we recall the ``story'' of abelian
S-ramification restricting ourselves to elementary aspects in order to precise
much basic contributions and references, often disregarded, which may be used
by specialists of other domains of number theory. Indeed, the torsion T\_(K,S)
of Gal(H\_(K,S)/K) (even if S=P) is a fundamental obstruction in many problems.
All relationships involving S-ramification, as Iwasawa's theory, Galois
cohomology, p-adic L-functions, elliptic curves, algebraic geometry, would
merit special developments, which is not the purpose of this text.
