"Source: Text/Geometry/Scheme.text";
"Line: 7202";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 7202
// Example: H122E56 ()
print "Example: H122E56";
ei := GetEchoInput();
SetEchoInput(true);
P<a,b,c,d,e> := ProjectiveSpace(RationalField(),4);
X := Scheme(P,[a*d + c*e, a*c + d*e,
 a^2 - e^2, c^2*e - d^2*e,
 b^2 + c*d + e^2]); // union of 3 irreducible curves
Dimension(X);
assert $1 eq 1;
time SecantVariety(X : PatchIndex := 2); 
Dimension($1);
assert $1 eq 3;
time IsInSecantVariety(X,P![0,1,0,-3,0]);
assert $1;
SetEchoInput(ei);
