"Source: Text/Ring/FldAb.text";
"Line: 594";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldAb.text, line: 594
// Example: H41E4 ()
print "Example: H41E4";
ei := GetEchoInput();
SetEchoInput(true);
k := NumberField([Polynomial([-10, 0, 1]), CyclotomicPolynomial(16)]);
k := OptimizedRepresentation(AbsoluteField(k));
o := MaximalOrder(k);
ClassGroup(o : Proof := "GRH");
IndependentUnits(o);
SetOrderUnitsAreFundamental(o);
p := &* [113, 193, 241];
r, mr := RayClassGroup(p*o);
#r; Ngens(r);
autk := Automorphisms(k);
time m1 := hom<r -> r | [ autk[2](mr(r.i))@@ mr : i in [1..Ngens(r)]]>;
time InducedAutomorphism(mr, autk[2], p);
p *:= 257*337;
r, mr := RayClassGroup(p*o);
#r; Ngens(r);
time m1 := hom<r -> r | [ autk[2](mr(r.i))@@ mr : i in [1..Ngens(r)]]>;
time InducedAutomorphism(mr, autk[2], p);
SetEchoInput(ei);
