default(new_galois_format, 1);
\\ 8: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
?? nflist
vK = nflist("C3", [1, 10^10]);
#vK
vK[1]
nfdisc(%)
nflist("C3", (7 * 13)^2)
vD = apply(nfdisc, vK);
nflist("J4", 1)
\\ 9: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
vK = nflist("S3", [1, 10^6]);
#vK
vK = nflist("S3", [1, 10^ 6]);
#vK
vKp = nflist("S3", [1, 10^ 6], 0);
#vKp
vKm = nflist("S3", [1, 10^ 6], 1);
#vKm
v = nflist("S3", [1, 10^ 6], -2);
apply(length, v)
\\ 10: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
??nfresolvent
v = nflist("S3", [1,10^7],,x^2+23)
apply(P -> issquare(nfdisc(P) / -23), v)
F = nflist("C3")[1]
nfdisc(F)
v = nflist("A4", [1,10^7],, F)
apply(P -> issquare(nfdisc(P) / 49), v)
\\ 12: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
Pt = nflist([8,1], 't)
{
L = List();
for (t = 1, 100,
P = subst(Pt, 't, t); if (!polisirreducible(P), next);
[n,s,k] = polgalois(P); if ([n,k] == [8,1], listput(~L, P)));
#L;
}
L = Set(apply(polredabs, L)); #L
D = apply(nfdisc, L); [vecmin(D), vecmax(D)]
\\ 13: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
OK(Pt, t, deg) =
{ my(P = subst(Pt, 't, t));
polisirreducible(P)
&& poldegree(nfsplitting(P, deg)) == deg;
}
Pt = nflist([12, 24], 't);
OK(Pt, 0, 48)
OK(Pt, 3, 48)
[OK(Pt, t, 48) | t <- [1..20]]
\\ 14: \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\
D = poldisc(Pt);
D /= gcd(D, D')
polrootsreal(D)
polsturm(subst(Pt,'t,-1))
polsturm(subst(Pt,'t, 2))