Tougher groups (2/4)
? Pt = nflist([8,1], ’t) \\ or "C8"
%1 = x^8 + (-4*t^4 - 4)*x^6 + (8*t^6 + 2*t^4 + 8*t^2 + 2)*x^4
+ (-4*t^8 - 4*t^6 - 4*t^4 - 4*t^2)*x^2 + (t^8 + t^4)
? 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; }
%2 = 100 \\ all our specializations happen to have the right group
? L = Set(apply(polredabs, L)); #L \\ remove duplicates
%3 = 100 \\ . . . no duplicates
? D = apply(nfdisc, L); [vecmin(D), vecmax(D)]
%4 = [2147483648, h64 digitsi] \\ large discriminants
PARI/GP day 2021 (02/06/2021) – p. 12/14