"Source: Text/Ring/RngOrd.text";
"Line: 6003";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 6003
// Example: H39E25 ()
print "Example: H39E25";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(Integers());
f := x^4-420*x^2+40000;
K<y> := NumberField(f);
E := EquationOrder(K);
O := MaximalOrder(K);
elt := O ! (y^2/40+y/4);
elt in E;
assert not $1;
I := ideal< O | elt >;
I;
FieldOfFractions(O)!!I;
O!!$1 eq I;
assert $1;
SetEchoInput(ei);
