# Singular Book 1.3.15 -- computing with radicals

 i1 : R = QQ[x,y,z]; i2 : radical ideal(z^4+2*z^2+1) 2 o2 = ideal(z + 1) o2 : Ideal of R
 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 $(y^2+y)^k \in I$.
 i5 : k = 0; i6 : while (y^2+y)^k % I != 0 do k = k+1; i7 : k o7 = 4