"Source: Text/Geometry/Scheme.text";
"Line: 444";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 444
// Example: H122E5 ()
print "Example: H122E5";
ei := GetEchoInput();
SetEchoInput(true);
k := Rationals();
P1<s,t> := ProjectiveSpace(k,1);
P2<x,y,z> := ProjectiveSpace(k,2);
f := map< P1 -> P2 | [s/t,s^2/(s^2 - t^2),t/s] >;
f;
IsRegular(f);
assert $1;
Image(f);
p := P1 ! [3,2];
f(p);
f(p) in Image(f);
S := Scheme(P2,x^2 - y*z);
Z := Pullback(f,S);
Z;
RationalPoints(Z);
P := PointsOverSplittingField(Z); P;
Ring(Universe($1));
SetEchoInput(ei);
