"Source: Text/Ring/FldFunG.text";
"Line: 3056";
"Date: Fri Sep 26 13:15:42 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/FldFunG.text, line: 3056
// Example: H46E23 ()
print "Example: H46E23";
ei := GetEchoInput();
SetEchoInput(true);
PF<x> := PolynomialRing(GF(13, 2));
P<y> := PolynomialRing(PF);
FF1<b> := ext<FieldOfFractions(PF) | y^2 - x>;
P<y> := PolynomialRing(FF1);
FF2<d> := ext<FF1 | y^3 - b>;
RER_FF2 := RationalExtensionRepresentation(FF2);
NumberOfPlacesOfDegreeOneECF(FF2) eq NumberOfPlacesOfDegreeOneECF(RER_FF2);
assert $1;
SerreBound(FF2);
assert $1 eq 170;
NumberOfPlacesDegECF(FF2, 1);
assert $1 eq 170;
_, P := HasPlace(FF2, 1);
P;
Degree(P) eq 1;
assert $1;
LPolynomial(FF2, 2) eq LPolynomial(RER_FF2, 2);
assert $1;
SetEchoInput(ei);
