//SINGULAR Example4.3.3

option(redSB);            //to obtain a reduced normal form 
ring R=0,(x,y),lp;            
ideal a1=x;               //preparation of the example 
ideal a2=y2+2y+1,x-1;
ideal a3=y2-2y+1,x-1;
ideal I=intersect(a1,a2,a3);
I;

ideal G=std(I);
indepSet(G);

ring S=(0,y),(x),lp;     //the zero ring K(u)[x\u]
ideal G=imap(R,G);
G;

setring R;
poly h=y4-2y2+1;       //the lcm of the leading coefficients

ideal I1=quotient(I,h);
I1;