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Macaulay2Doc > basic commutative algebra > M2SingularBook > Singular Book 1.8.15

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.