COMPUTING PRIMARY DECOMPOSITION OF ZERO-DIMENSIONAL IDEALS OVER FINITE FIELDS

Gao et al. [3] have described an algorithm for computing primary decomposition of zero-dimensional ideals over finite field Fpk where p is a prime and k is an integer. They have used invariant subspace (over Fpk ) of the Frobenius map t 7! tpk in their algorithm. In this paper, we show that instead of this map, we can use the invariant subspace (over Fp) of the map t 7! tp. Our algorithm makes use of Gr¨obner bases method for computeing a basis for the nullspace of this subspace and also finding the component of the input ideal