"Source: Text/Geometry/Scheme.text";
"Line: 4071";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 4071
// Example: H122E22 ()
print "Example: H122E22";
ei := GetEchoInput();
SetEchoInput(true);
A<x,y> := AffineSpace(Rationals(),2);
C := Curve(A,x^2 + y^2);
IsIrreducible(C);
assert $1;
D := Curve(A,x - 1);
IntersectionPoints(C,D);
Qi<i> := QuadraticField(-1);
IntersectionPoints(C,D,Qi);
B<u,v> := BaseChange(A,Qi);
C1 := BaseChange(C,B);
D1 := BaseChange(D,B);
IsIrreducible(C1);
assert not $1;
IntersectionPoints(C1,D1);
PrimeComponents(C1);
SetEchoInput(ei);
