"Source: Text/Geometry/Scheme.text";
"Line: 6065";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 6065
// Example: H122E43 ()
print "Example: H122E43";
ei := GetEchoInput();
SetEchoInput(true);
k := GF(7);
P<x,y,z> := ProjectiveSpace(k,2);
p := x^2 + y^2;                            
f := map< P -> P | [p*x,p*y,z^2*(z-x)] >;
BasePoints(f);
Degree(BaseScheme(f)); 
assert $1 eq 6;
HasPointsOverExtension(BaseScheme(f));   
assert $1;
BasePoints(f,ext<k|2>);
HasPointsOverExtension(BaseScheme(f),ext<k|2>);
assert not $1;
SetEchoInput(ei);
