//SINGULAR Example 1.8.18


ring A=0,(x,y,z),dp;
ring B=0,(a,b),dp;
map phi=A,a2,ab,b2;
ideal zero;               //compute the preimage of 0
setring A;
preimage(B,phi,zero);     //the built-in SINGULAR command

ring C=0,(x,y,z,a,b), dp; //the method described above
ideal H=x-a2, y-ab, z-b2;
eliminate(H,ab);