//SINGULAR Example 1.3.3



ring S = 0,(a,b,c),lp;
ring R = 0,(x,y,z),dp;
ideal i = x, y, x2-y3;
map phi = S,i;     //a map from S to R, a->x, b->y, c->x2-y3
LIB "algebra.lib"; //load algebra.lib

is_injective(phi,S);

ideal j = x, x+y, z-x2+y3;
map psi = S,j;                  //another map from S to R
is_injective(psi,S);

alg_kernel(phi,S);

alg_kernel(psi,S);

ideal Z;                    //the zero ideal in R
setring S;
preimage(R,phi,Z);          //computes kernel of phi in S

setring R;
is_surjective(psi,S);

is_bijective(psi,S);        //faster than is_injective, 
                            //is_surjective