Given a prime ideal I in a polynomial ring over a field of positive characteristic, and an integer n, this method returns the n-th symbolic power of I. To compute I(a), find the largest value k with q = pk ≤a. Then I(a) = (I[q] : Ia-q+1).
i1 : B = ZZ/7[x,y,z]; |
i2 : f = map(ZZ/7[t],B,{t^3,t^4,t^5}) ZZ 3 4 5 o2 = map(--[t],B,{t , t , t }) 7 ZZ o2 : RingMap --[t] <--- B 7 |
i3 : I = ker f; o3 : Ideal of B |
i4 : symbPowerPrimePosChar(I,2) 4 2 2 2 2 3 3 2 2 3 3 2 4 3 2 5 3 2 3 o4 = ideal (y - 2x*y z + x z , x y - x y*z - y z + x*z , x y - x z - y z + x*y*z , x + x*y - 3x y*z + z ) o4 : Ideal of B |
The ideal must be prime.