//SINGULAR Example 1.8.1


ring A  = 0,(x,y),dp;       
ideal I = x10+x9y2,y8-x2y7;
ideal J = std(I);
poly f  = x2y7+y14;

reduce(f,J,1);      //3rd parameter 1 avoids tail reduction
f=xy13+y12;
reduce(f,J,1); 

ideal K = f,x2y7+y14;
reduce(K,J,1);      //normal form for each generator of K

K=f,y14+xy12;
size(reduce(K,J,1));          //result is 0 iff K is in I