kk=ZZ
R=kk[x1,x2,x3,f1,f2,f3,L1,L2,L3,y1,y2,y3] I=ideal(L1*x2*x3-(x2^2+f2*f3*x3^2+f3*x1^2),L2*x3*x1-(x3^2+f3*f1*x1^2+f1*x2^2),L3*x1*x2-(x1^2+f1*f2*x2^2+f2*x3^2),y1*x1-(f1*L1^2+(f1*f2*f3-1)^2),y2*x2-(f2*L2^2+(f1*f2*f3-1)^2),y3*x3-(f3*L3^2+(f1*f2*f3-1)^2))
J=saturate(I,x1*x2*x3)
S=R/J
d=x1*x2*x3
D=ideal(x1*x2*x3,(x3*L2-f3*f1*x1)*x2*x3,x1*(x1*L3-f1*f2*x2)*x3,x1*x2*(x2*L1-f2*f3*x3))
n=1
D'=ideal(d^n)
M=saturate(D',D)
D'==M