"Source: Text/Geometry/Scheme.text";
"Line: 351";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 351
// Example: H122E4 ()
print "Example: H122E4";
ei := GetEchoInput();
SetEchoInput(true);
P<x,y,z> := ProjectiveSpace(Rationals(),2);
A := AffinePatch(P,3);
A;
A<u,v> := A;
A;
P eq Codomain(ProjectiveClosureMap(A));
assert $1;
X := Scheme(A,[u^2-v^3,u^2+v^3]);
PX := ProjectiveClosure(X);
PX;
AffinePatch(PX,3) eq X;                    // (1)
assert $1;
aX1:=AffinePatch(PX,1);
IsEmpty(aX1);                              // (2)
assert $1;
ProjectiveClosure(aX1) eq PX;              // (2)
assert $1;
Y := Scheme(P,[x*y^2-z^3,x*y^2+z^3]);
AffinePatch(Y,3);
AffinePatch(Y,3) eq X;                     // (3)
assert $1;
Y eq PX;
assert not $1;
p := A ! [0,0];
PX ! p;
SetEchoInput(ei);
