Singular Book 1.3.15 -- computing with radicals

Compute the radical of an ideal with radical.

i1 : R = QQ[x,y,z];

i2 : radical ideal(z^4+2*z^2+1)

            2
o2 = ideal(z  + 1)

o2 : Ideal of R

A somewhat more complicated example:

i3 : I = ideal"xyz,x2,y4+y5"

                    2   5    4
o3 = ideal (x*y*z, x , y  + y )

o3 : Ideal of R

i4 : radical I

                   2
o4 = ideal (-x, - y  - y)

o4 : Ideal of R

The index of nilpotency. We compute the minimal integer k such that (y²+y)^k ∈I.

i5 : k = 0;

i6 : while (y^2+y)^k % I != 0 do k = k+1;

i7 : k

o7 = 4

The index of nilpotency is 4.