"Source: Text/Ring/FldFunAb.text";
"Line: 348";
"Date: Fri Sep 26 12:10:11 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunAb.text, line: 348
// Example: H47E3 ()
print "Example: H47E3";
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]>;
q, mq := quo<R | U1>;
l4 := [ x`subgroup : x in Subgroups(q : Quot := [4])];
#l4;
assert $1 eq 7168;
A := [AbelianExtension(D, x@@mq) : x in l4];
s4 := [<Genus(a), NumberOfPlacesOfDegreeOne(a), a> : a in A];
Maximum([x[2]/x[1] : x in s4]);
E := FunctionField(s4[15][3]);
MaximalOrderFinite(s4[15][3]);
MaximalOrderInfinite(s4[15][3]);
SetEchoInput(ei);
