"Source: Text/Ring/RngOrdGal.text";
"Line: 903";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrdGal.text, line: 903
// Example: H40E4 ()
print "Example: H40E4";
ei := GetEchoInput();
SetEchoInput(true);
Z:= Integers();
P<x>:= PolynomialRing(Z);
G, R, S := GaloisGroup(x^6-108);
G;
R;
S;
time G, _, S := GaloisGroup(x^32-x^16+2);
#G;
assert $1 eq 2048;
SetEchoInput(false);
load galpols;
SetEchoInput(true);
f := PolynomialWithGaloisGroup(9, 14);
G := GaloisGroup(f);
TransitiveGroupIdentification(G);
M := MaximalOrder(f);
kM := FieldOfFractions(M);
f:= Factorisation(Polynomial(kM, f))[2][1];
f;
g, r, p:= GaloisGroup(f);
TransitiveGroupIdentification(g);
Subgroups(G:OrderEqual := #g);
IsIsomorphic(g, $1[1]`subgroup);
SetEchoInput(ei);
