"Source: Text/Geometry/Scheme.text";
"Line: 527";
"Date: Fri May 26 16:23:18 2023";
"Main: Thu May 25 10:02:38 2023";
// original file: Text/Geometry/Scheme.text, line: 527
// Example: H119E6 ()
print "Example: H119E6";
ei := GetEchoInput();
SetEchoInput(true);
Q := RationalField();
P<x,y,z> := ProjectiveSpace(Q,2);
L := LinearSystem(P,2);
L;
Sections(L);
P5<u0,u1,u2,u3,u4,u5> := ProjectiveSpace(Q,5);
phi := map< P -> P5 | Sections(L) >;
Image(phi);
p := P ! [3,2,1];
L1 := LinearSystem(L, p);
L1;
P4<v0,v1,v2,v3,v4> := ProjectiveSpace(Q,4);
phi := map< P -> P4 | Sections(L1) >;
Image(phi);
M := Matrix(3,[v0, v1 + (2*v3 - 3*v4), v3, v1 - (2*v3 - 3*v4), v2, v4]);
Minors(M,2);
ideal< CoordinateRing(P4) | $1 > eq Ideal(Image(phi));
assert $1;
SetEchoInput(ei);
