# Singular Book 1.8.15 -- saturation

 i1 : A = QQ[x,y,z]; i2 : I1 = ideal(x^5*z^3, x*y*z, y*z^4); o2 : Ideal of A i3 : saturate(I1,z) 5 o3 = ideal (y, x ) o3 : Ideal of A
Now we compute the saturation using a loop.
 i4 : J = I1:z 3 5 2 o4 = ideal (x*y, y*z , x z ) o4 : Ideal of A i5 : k = 0; i6 : while not isSubset(J,I1) do ( k = k+1; I1 = J; J = I1 : z; ); i7 : J 5 o7 = ideal (y, x ) o7 : Ideal of A i8 : k o8 = 4
We needed to use quotient four times.