Easy groups (4/4)
In the form nflist(G) one gets a few fields, about 10, of smallish discriminant (no guarantee
they will have minimal discriminants).
A final optional argument allows to impose a resolvent field in the galois closure K̂ (see
??nfresolvent for definitions):
? v = nflist("S3", [1,10^7], , x^2+23) \\ impose Q(
√
−23) ⊂ K̂
? apply(P -> issquare(nfdisc(P) / -23), v) \\ disc(K) = −23f2
%2 = [1, 1, ..., 1]
? F = nflist("C3")[1] \\ some cyclic cubic field F
? nfdisc(F)
%4 = 49 \\ . . . actually of smallest discriminant
? v = nflist("A4", [1,10^7], , F) \\ F ⊂ K̂
? apply(P -> issquare(nfdisc(P) / 49), v)
%6 = [1, 1, ..., 1]
PARI/GP day 2021 (02/06/2021) – p. 10/14