"Source: Text/Ring/FldFunAb.text";
"Line: 283";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunAb.text, line: 283
// Example: H47E2 ()
print "Example: H47E2";
ei := GetEchoInput();
SetEchoInput(true);
k<w> := GF(4);
kt<t> := PolynomialRing(k);
ktx<x> := PolynomialRing(kt);
K := FunctionField(x^3-w*t*x^2+x+t);
lp := Places(K, 2);
D := 4*lp[2]+2*lp[6];
R, mR := RayClassGroup(D);
inf := InfinitePlaces(K);
U1 := sub<R | [x@@ mR : x in inf]>;
U2 := sub<R | [5*R.i : i in [1..Ngens(R)]]>;
U3 := sub<R | U1, U2>;
A := AbelianExtension(D, U3);
A;
FunctionField(A);
E := $1;
MaximalOrderFinite(A);
MaximalOrderInfinite(A);
DiscriminantDivisor(A);
$1 eq Divisor(Discriminant($3)) + Divisor(Discriminant($2));
assert $1;
SetEchoInput(ei);
