//SINGULAR Example4.2.8

option(redSB);       //to obtain a reduced normal form
ring R=0,(x,y),lp;
ideal I=(y2-1)^2,x2-(y+1)^3;
map phi=R,x,x+y;     //we choose a generic coordinate change
map psi=R,x,-x+y;    //and the inverse map
I=std(phi(I));
I;

factorize(I[1]);

ideal Q1=std(I,(y2-2y-7)^2); //the candidates for the 
                             //primary ideals
ideal Q2=std(I,(y+1)^3);     //in general position
Q1;
Q2;

factorize(Q1[1]);   //test for primary and in general 
                    //position for Q1 
factorize(Q2[1]);   //test for primary and in general 
                    //position for Q2 

Q1=std(psi(Q1));      //the inverse coordinate change
Q2=std(psi(Q2));      //the result
Q1;
Q2;