"Source: Text/Ring/FldFunG.text";
"Line: 8068";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 8068
// Example: H46E44 ()
print "Example: H46E44";
ei := GetEchoInput();
SetEchoInput(true);
k<w> := GF(9);
R<x> := FunctionField(k);
P<y> := PolynomialRing(R);
f := y^4 + (2*x^5 + x^4 + 2*x^3 + x^2)*y^2 +
            x^8 + 2*x^6 + x^5 + x^4 + x^3 + x^2;
F<a> := FunctionField(f);
D1 := Zeros(a)[1] - Poles(F!x)[1];
D2 := Zeros(a)[4] - Poles(F!x)[2];
G,mapfromG,maptoG:=ClassGroup(F : Proof:=false);
Order(maptoG(D1));
assert $1 eq 48;
Order(maptoG(D2));
assert $1 eq 336;
TateLichtenbaumPairing(D1,D2,48);
TateLichtenbaumPairing(D2,D1,336);
SetEchoInput(ei);
