//SINGULAR ExampleA.7.16



ring R = 0,(t,s,x,y),(dp(1),dp);
ideal I = x-t2,y-t3;//ideal of the graph of f
eliminate(I,t);

ideal J = std(I);   //Groeber basis w.r.t. a correct ordering
J;

ring R1 = (0,x,y),(t,s),dp;       
ideal Jh = homog(imap(R,J),s);

setring R;          //go back to R
ideal Jh= imap(R1,Jh);             
Jh;                 //ideal of the closure of the graph of f

std(subst(Jh,t,1,s,0));  //points at infinity of the closure 

ring S = 0,(t,s,x,y),(dp(1),dp);
ideal I = xt-1,y;             //ideal of the affine hyperbola
eliminate(I,t);             

ideal J = std(I); 
ring S1 = (0,x,y),(t,s),dp;   //homogenize J as ideal of     
ideal Jh = homog(imap(S,J),s);//polynomials in t only
setring S;                      
ideal Jh = imap(S1,Jh);       //go back to original ring      
Jh;

std(subst(Jh,t,1,s,0));       //intersection with infinity