//SINGULAR Example4.2.6

option(redSB);       //to obtain a reduced normal form
ring R=0,(x,y),lp;
ideal I=y4-4y3-10y2+28y+49,x3-6x2y+3x2+12xy2-12xy+3x-8y3
+13y2-8y-6;
//the generators are a Groebner basis

factorize(I[1]);     //to test whether Criterion 4.2.4 
                     //(2.1) holds
ideal prim=std(y2-2y-7);
poly q=3x-6y+3;
poly f2=I[2];
reduce(q^3-27*f2,prim);