galoisgetpol

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 \kbd{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 current version of \kbd{galpol} supports groups of order $a\leq 143$.
 The output is a vector [\kbd{pol}, \kbd{den}] where

 \item  \kbd{pol} is the polynomial of degree $a$

 \item \kbd{den} is the denominator of \kbd{nfgaloisconj(pol)}.
 Pass it as an optional argument to \tet{galoisinit} or \tet{nfgaloisconj} to
 speed them up:
 \bprog
 ? [pol,den] = galoisgetpol(64,4,1);
 ? G = galoisinit(pol);
 time = 352ms
 ? galoisinit(pol, den);  \\ passing 'den' speeds up the computation
 time = 264ms
 ? % == %`
 %4 = 1  \\ same answer
 @eprog
 If $b$ and $s$ are omitted, return the number of isomorphism classes of
 groups of order $a$.
Variant: Also available is \fun{GEN}{galoisnbpol}{long a} when $b$ and $s$
 are omitted.