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))