//SINGULAR ExampleA.2.14





LIB "algebra.lib";
ring R = 0,(x,y,z),dp;
qring Q = std(z-x2+y3);     //quotient ring R/<z-x2+y3>

ring S = 0,(a,b,c,d),dp; 
map psi = R,a,a+b,c-a2+d3;  //a map from R to S,
                            //x->a, y->a+b, z->c-a2+d3  
is_injective(psi,R);               
is_surjective(psi,R);   

qring T = std(ideal(d,c-a2+b3));   //quotient ring S/<d,c-a2+b3>
map chi = Q,a,b,a2-b3;      //map Q --> T between two 
                            //quotient rings,
                            //x->a, y->b, z->a2-b3
is_bijective(chi,Q);