"Source: Text/Geometry/Scheme.text";
"Line: 7820";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 7820
// Example: H122E64 ()
print "Example: H122E64";
ei := GetEchoInput();
SetEchoInput(true);
K := Rationals();
R := PolynomialRing(K, 5, "grevlex");
P := ProjectiveSpace(R);
d := 5;
s := [ &+[R.i^(d+j) : i in [1..5]]:j in [1..3] ];
X := Scheme(P, s : Saturated := true);
s := Sections(LinearSystem(P, d+4));
s := [ &+[Random(1,10)*q : q in s] : i in [1 .. #s-30]];
time L := LinearSystem(P, s);
time J := LinearSystem(L, X);
J;
// If L is complete, the computation is faster.
L := LinearSystem(P, d+4);
time J := LinearSystem(L,X);
J;
SetEchoInput(ei);
