//SINGULAR Example4.4.10

//========================== we need==============================
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);
poly h=y4-2y2+1;       //the lcm of the leading coefficients
ideal I1=quotient(I,h);
//================================================================


ideal I2=quotient(I,I1);
I2;