//SINGULAR Example4.3.5 //===================== we need ================================ option(redSB); //to obtain a reduced normal form ring R=0,(x,y),lp; ideal a1=x; //preparation of the example ideal a2=y2+2y+1,x-1; ideal a3=y2-2y+1,x-1; ideal I=intersect(a1,a2,a3); poly h=y4-2y2+1; //the lcm of the leading coefficients ideal I1=quotient(I,h); //============================================================== ideal I2=std(I+ideal(h)); //we compute now the decomposition of I2 indepSet(I2); list fac=factorize(I2[1]); fac; ideal J1=std(I2,(y+1)^2); //the two candidates ideal J2=std(I2,(y-1)^2); //for primary ideals J1; J2; map phi=R,x,x+y; map psi=R,x,-x+y; //and the inverse map ideal K1=std(phi(J1)); ideal K2=std(phi(J2)); factorize(K1[1]); ideal K11=std(K1,(y+1)^2); //the new candidates //for primary ideals ideal K12=std(K1,(y+2)^2); //coming from K1 factorize(K2[1]); ideal K21=std(K2,(y-1)^2); //the new candidates // for primary ideals ideal K22=std(K2,y2); //coming from K2 K11=std(psi(K11)); //the inverse coordinate //transformation K12=std(psi(K12)); K21=std(psi(K21)); K22=std(psi(K22)); K11; //the result K12; K21; K22;