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SymbolicPowers :: symbPowerPrimePosChar

symbPowerPrimePosChar

Synopsis

Description

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 
o4 = ideal (y  - 2x*y z + x z , x y  - x y*z - y z  + x*z , x y  - x z - y z
     ------------------------------------------------------------------------
            2   5      3     2       3
     + x*y*z , x  + x*y  - 3x y*z + z )

o4 : Ideal of B

Caveat

The ideal must be prime.

See also

Ways to use symbPowerPrimePosChar :