//SINGULAR Example 1.3.15



ring R = 0,(x,y,z),dp;
poly p =  z4+2z2+1;
LIB "primdec.lib";           //loads library for radical
radical(p);                  //square free part of p

ideal I = xyz, x2, y4+y5;    //a more complicated ideal
radical(I);

ideal Is = groebner(I);
int k;
while (reduce((y2+y)^k,Is) != 0 ) {k++;}
k;