"Source: Text/Geometry/Scheme.text";
"Line: 2086";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 2086
// Example: H122E14 ()
print "Example: H122E14";
ei := GetEchoInput();
SetEchoInput(true);
P<u,v,w> := ProjectiveSpace(GF(11),2);
C := Scheme(P,u^2 + u*w + 6*v^2);
Z := Scheme(C,[u,v]);
IsSubscheme(Z,C);
assert $1;
D := Scheme(P,2*u^2 + 2*u*w + v^2);
D eq C;
assert $1;
IsSubscheme(C,D) and IsSubscheme(D,C);
assert $1;
DefiningIdeal(D) eq DefiningIdeal(C);
assert $1;
DefiningPolynomial(D) eq DefiningPolynomial(C);
assert not $1;
X<r,s,t> := ProjectiveSpace(GF(11),2);
E := Scheme(P,r^2 + r*s + 6*t^2);
E eq C;
assert not $1;
SetEchoInput(ei);
