"Source: Text/Ring/FldFunG.text";
"Line: 9423";
"Date: Thu Jun 16 15:04:46 2022";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Ring/FldFunG.text, line: 9423
// Example: H45E57 ()
print "Example: H45E57";
ei := GetEchoInput();
SetEchoInput(true);
k := GF(13);
A<t> := PolynomialRing(k);
Ax<x> := PolynomialRing(A);
f := x^5 + (t^2 + 2*t + 1)*x^4 + (t^4 + 4*t^3 + 6*t^2 + 4*t + 1)*x^3 + (t^3   
        + 3*t^2 + 3*t + 1)*x^2 + (t^4 + 4*t^3 + 6*t^2 + 4*t + 1)*x + t;
L := FunctionField(f);
I := OMRepresentation(L,[1/L.1^2,12]);
I;
TwoElement(I);
Norm(I);
Factorization(I);
Montes(L, t+1);
Valuation(I, L`PrimeIdeals[t][1]);
Valuation(I, L`PrimeIdeals[t+1][1]);
SetEchoInput(ei);
