"Source: Text/Geometry/Sheaf.text";
"Line: 355";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Sheaf.text, line: 355
// Example: H123E2 ()
print "Example: H123E2";
ei := GetEchoInput();
SetEchoInput(true);
P3<x,y,z,t> := ProjectiveSpace(Rationals(),3);
X := Scheme(P3,[
y^3 - y*z^2 - 2*y^2*t - 2*x*z*t - 3*y*z*t + z^2*t - y*t^2 + 2*z*t^2 + 2*t^3,
x^2*z + x*z^2 + y*z^2 + 3*x*z*t + 2*y*z*t - z^2*t + y*t^2 - 2*z*t^2 - 2*t^3,
y^2*z - y*z^2 + y^2*t - x*z*t - 4*y*z*t + z^2*t - 3*y*t^2 + 2*z*t^2 + 2*t^3,
x*y - x*z - x*t + y*t]);
OX := StructureSheaf(X);
M1 := Module(OX);
M2 := FullModule(OX);
h1 := HilbertSeries(M1); h1;
h2 := HilbertSeries(M2); h2;
h2-h1;
SetEchoInput(ei);
