"Source: Text/Geometry/Scheme.text";
"Line: 1008";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 1008
// Example: H122E8 ()
print "Example: H122E8";
ei := GetEchoInput();
SetEchoInput(true);
Q := RationalField();
P2<x,y,z> := ProjectiveSpace(Q,2);
E := Curve(P2,y^2*z-x^3-x^2*z-z^3);
ExE := SegreProduct([E,E]);
P8<a,b,c,d,e,f,g,h,i> := Ambient(ExE);
ExE;
// or we could have started with ExE in product projective space
P22<x,y,z,s,t,u> := ProductProjectiveSpace(Q,[2,2]);
EE := Scheme(P22,[y^2*z-x^3-x^2*z-z^3, t^2*u-s^3-s^2*u-u^3]);
EE;
ExE_1 := SegreEmbedding(EE);
// transfer ExE_1 to the Ambient of ExE to compare
ExE_1 := Scheme(P8,[Evaluate(pol,[a,b,c,d,e,f,g,h,i]) : pol in 
            DefiningPolynomials(ExE_1)]);
ExE eq ExE_1;
assert $1;
SetEchoInput(ei);
