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 $q = p^k \leq a$. Then $I^{(a)} = (I^{[q]} : I^{a-q+1})$.
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.
The object symbPowerPrimePosChar is a method function.