"Source: Text/Geometry/AlgSrf.text";
"Line: 5107";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/AlgSrf.text, line: 5107
// Example: H126E28 ()
print "Example: H126E28";
ei := GetEchoInput();
SetEchoInput(true);
Q := Rationals();
P3<x,y,z,w> := ProjectiveSpace(Q, 3);
P2<X,Y,Z> := ProjectiveSpace(Q, 2);
X := Scheme(P3, x^2*z^2 - x*y^3 - x*y*z*w + 2*y^2*w^2 - z*w^3);
pencil := map<X -> P2 | [x*y - w^2, y^2 - z*w, x*z - y*w]>;
DefiningPolynomial(Image(pencil));
ParametrizePencil(pencil, P2);
SetEchoInput(ei);
