"Source: Text/Geometry/Crv.text";
"Line: 1045";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Crv.text, line: 1045
// Example: H124E3 ()
print "Example: H124E3";
ei := GetEchoInput();
SetEchoInput(true);
A<x,y,z> := ProjectiveSpace(Rationals(),2);
C := Curve(A,z*y^2 - x^3 - x*z^2 - z^3);   
IsNonsingular(C);                          
assert $1;
DefiningIdeal(C);
IsPrincipal($1);
M := HessianMatrix(C);
Determinant(M);
D := Curve(A,Determinant(M));
IntersectionPoints(C,D);
SetEchoInput(ei);
