Function: galoisgetpol
Section: number_fields
C-Name: galoisgetpol
Prototype: LD0,L,D1,L,
Description:
 (small):int               galoisnbpol($1)
 (small,):int              galoisnbpol($1)
 (small,,):int             galoisnbpol($1)
 (small,small,small):vec   galoisgetpol($1, $2 ,$3)
Help: galoisgetpol(a,{b},{s}): Query the galpol package for a polynomial with
 Galois group isomorphic to GAP4(a,b), totally real if s=1 (default) and
 totally complex if s=2.  The output is a vector [pol, den] where pol is the
 polynomial and den is the common denominator of the conjugates expressed
 as a polynomial in a root of pol. If b and s are omitted, return the number of
 isomorphism classes of groups of order a.
Doc: Query the galpol package for a polynomial with Galois group isomorphic to
 GAP4(a,b), totally real if $s=1$ (default) and totally complex if $s=2$. The
 output is a vector [\kbd{pol}, \kbd{den}] where \kbd{pol} is the polynomial and
 \kbd{den} is the common denominator of the conjugates expressed as a
 polynomial in a root of \kbd{pol}, which can be passed as an optional argument
 to \tet{galoisinit} and \tet{nfgaloisconj} as follows:
 \bprog
 V=galoisgetpol(8,4,1);
 G=galoisinit(V[1], V[2])  \\ passing V[2] speeds up the computation
 @eprog

 If $b$ and $s$ are omitted, return the number of isomorphic class of groups
 of order $a$.
Variant: Also available is \fun{GEN}{galoisnbpol}{long a} when $b$ and $s$
 are omitted.
