1Function: galoisgetpol
2Section: number_fields
3C-Name: galoisgetpol
4Prototype: LD0,L,D1,L,
5Description:
6 (small):int               galoisnbpol($1)
7 (small,):int              galoisnbpol($1)
8 (small,,):int             galoisnbpol($1)
9 (small,small,small):vec   galoisgetpol($1, $2 ,$3)
10Help: galoisgetpol(a,{b},{s}): query the galpol package for a polynomial with
11 Galois group isomorphic to GAP4(a,b), totally real if s=1 (default) and
12 totally complex if s=2.  The output is a vector [pol, den] where pol is the
13 polynomial and den is the common denominator of the conjugates expressed
14 as a polynomial in a root of pol. If b and s are omitted, return the number of
15 isomorphism classes of groups of order a.
16Doc: Query the \kbd{galpol} package for a polynomial with Galois group
17 isomorphic to
18 GAP4(a,b), totally real if $s=1$ (default) and totally complex if $s=2$.
19 The current version of \kbd{galpol} supports groups of order $a\leq 143$.
20 The output is a vector [\kbd{pol}, \kbd{den}] where
21
22 \item  \kbd{pol} is the polynomial of degree $a$
23
24 \item \kbd{den} is the denominator of \kbd{nfgaloisconj(pol)}.
25 Pass it as an optional argument to \tet{galoisinit} or \tet{nfgaloisconj} to
26 speed them up:
27 \bprog
28 ? [pol,den] = galoisgetpol(64,4,1);
29 ? G = galoisinit(pol);
30 time = 352ms
31 ? galoisinit(pol, den);  \\ passing 'den' speeds up the computation
32 time = 264ms
33 ? % == %`
34 %4 = 1  \\ same answer
35 @eprog
36 If $b$ and $s$ are omitted, return the number of isomorphism classes of
37 groups of order $a$.
38Variant: Also available is \fun{GEN}{galoisnbpol}{long a} when $b$ and $s$
39 are omitted.
40