Function: bnrisgalois
Section: number_fields
C-Name: bnrisgalois
Prototype: lGGG
Help: bnrisgalois(bnr,gal,H): check whether the class field attached to
 the subgroup H is Galois over the subfield of bnr.nf fixed by the Galois
 group gal, which can be given as output by galoisinit, or as a matrix or a
 vector of matrices as output by bnrgaloismatrix. The ray class field
 attached to bnr need to be Galois, which is not checked.
Doc: check whether the class field attached to the subgroup $H$ is Galois
 over the subfield of \kbd{bnr.nf} fixed by the group \var{gal}, which can be
 given as output by \tet{galoisinit}, or as a matrix or a vector of matrices as
 output by \kbd{bnrgaloismatrix}, the second option being preferable, since it
 saves the recomputation of the matrices.  Note: The function assumes that the
 ray class field attached to \var{bnr} is Galois, which is not checked.

 In the following example, we lists the congruence subgroups of subextension of
 degree at most $3$ of the ray class field of conductor $9$ which are Galois
 over the rationals.

 \bprog
 ? K = bnfinit(a^4-3*a^2+253009); B = bnrinit(K,9); G = galoisinit(K);
 ? [H | H<-subgrouplist(B,3), bnrisgalois(B,G,H)];
 time = 160 ms.
 ? M = bnrgaloismatrix(B,G);
 ? [H | H<-subgrouplist(B,3), bnrisgalois(B,M,H)]
 time = 1 ms.
 @eprog
 The second computation is much faster since \kbd{bnrgaloismatrix(B,G)} is
 computed only once.
