"Source: Text/Geometry/Scheme.text";
"Line: 1604";
"Date: Thu Sep 25 14:47:45 2025";
"Main: Fri Sep 26 14:29:19 2025";
// original file: Text/Geometry/Scheme.text, line: 1604
// Example: H122E12 ()
print "Example: H122E12";
ei := GetEchoInput();
SetEchoInput(true);
A2<x,y>:=AffineSpace(Rationals(),2);
C:=Scheme(A2,(x*y)); //union of the x- and y-axis
X2:=Scheme(A2,x^2);  //y-axis with double multiplicity
Difference(X2,C); //y-axis with mult. 1.
O:=Scheme(A2,[x,y]);
Difference(C,O);   
Difference(C,A2);     
A3<x,y,z>:= AffineSpace(Rationals(),3);
C:=Scheme(A3,Ideal([x,z])*Ideal([y,z])); //again, union of x- and y-axis
Z:=Scheme(A3,[z]); //the x,y plane
Difference(C,Z); 
SetEchoInput(ei);
