"Source: Text/Ring/RngOrd.text";
"Line: 2949";
"Date: Fri Sep 26 14:51:59 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Ring/RngOrd.text, line: 2949
// Example: H39E15 ()
print "Example: H39E15";
ei := GetEchoInput();
SetEchoInput(true);
R<x> := PolynomialRing(Integers());
f := x^4 - 420*x^2 + 40000;
K<y> := NumberField(f);
O := MaximalOrder(K);
B := Basis(O);
B[2];
T := MultiplicationTable(O);
T[2];
 &+[ T[2][3][i]*B[i] : i in [1..4] ];
B[2]*B[3];
TraceMatrix(O);
MatrixRing(RationalField(), 4) ! [Trace(B[i]*B[j]): i, j in [1..4] ];
SetEchoInput(ei);
