"Source: Text/Geometry/Scheme.text";
"Line: 7689";
"Date: Fri May 26 16:23:18 2023";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Geometry/Scheme.text, line: 7689
// Example: H119E61 ()
print "Example: H119E61";
ei := GetEchoInput();
SetEchoInput(true);
P<x,y,z,t> := ProjectiveSpace(Rationals(),3);
L := LinearSystem(P,3);
X := Scheme(P,[x*z-y^2,x*t-y*z,y*t-z^2]);
#Sections(L);
assert $1 eq 20;
L1 := LinearSystemTrace(L,X);
#Sections(L1);
assert $1 eq 10;
P1<u,v> := ProjectiveSpace(BaseRing(P),1);
phi := map< P1 -> P | [u^3,u^2*v,u*v^2,v^3] >;
Ideal(phi(P1)) eq Ideal(X);
assert $1;
Pullback(phi,L) eq Pullback(phi,L1);
assert $1;
Pullback(phi,L1);
SetEchoInput(ei);
