"Source: Text/Ring/FldFunG.text";
"Line: 4855";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 4855
// Example: H46E32 ()
print "Example: H46E32";
ei := GetEchoInput();
SetEchoInput(true);
F<z> := GF(13, 3);
PF<x> := PolynomialRing(F);
P<y> := PolynomialRing(PF);
FF1<b> := ext<FieldOfFractions(PF) | y^2 - x>;
P<y> := PolynomialRing(FF1);
FF2<d> := ext<FF1 | y^3 - ConstantField(FF1).1>;
ProductRepresentation([Random(FF2, 2) : i in [1 .. 3]], [2, 3, 2]);
ProductRepresentation($1);
r := Random(FF2, 3);
RationalFunction(r);
RationalFunction(r, CoefficientField(FF2));
RationalFunction(r, PF);                   
Differentiation(FF2!x, r);
Differentiation(FF2!b, r);
MFR2I := MaximalOrderInfinite(FF2);
Different(Numerator(r, MFR2I));    
SetEchoInput(ei);
