"Source: Text/Geometry/Scheme.text";
"Line: 5844";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 5844
// Example: H122E40 ()
print "Example: H122E40";
ei := GetEchoInput();
SetEchoInput(true);
P1<s,t> := ProjectiveSpace(Rationals(),1);
P3<w,x,y,z> := ProjectiveSpace(Rationals(),3);
f := map< P1 -> P3 | [s^4,s^3*t,s*t^3,t^4] >;
p := P1 ! [2,1];
f(p);
K := QuadraticField(5);
g := f(K);
ims := [];
for i in [1..100] do
Append(~ims, g(P1 ! [i,1]));
end for;
pts := [ P1 ! [i,1] : i in [1..100] ];
f(pts) eq ims;
assert $1;
P2<X,Y,Z> := ProjectiveSpace(Rationals(),2);
E := Curve(P2,Y^2*Z-X^3-X*Z^2);
p := E![0,0,1];
f := map<E->P1|[X,Y]>;
p in BaseScheme(f);
f(p);
SetEchoInput(ei);
