Tougher groups (3/4)
N.B. polgalois does not support n > 11. To check whether the specialization has the
expected Galois group (within PARI/GP), we can check whether it is irreducible in Q[x] then use
nfsplitting to check whether the Galois closure has the expected degree.
? OK(Pt, t, deg) =
{ my(P = subst(Pt, ’t, t));
polisirreducible(P)
&& poldegree(nfsplitting(P, deg)) == deg;
}
? Pt = nflist([12, 24], ’t); \\ C2 × S4
? OK(Pt, 0, 48)
%3 = 0
? OK(Pt, 3, 48);
%4 = 1
? [OK(Pt, t, 48) | t <- [1..20]]
%5 = [0, 0, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 0, 1, 1, 1, 1]
PARI/GP day 2021 (02/06/2021) – p. 13/14