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