An Improving Primary Decomposition of Zero-dimensional Ideals over Finite Fields

Details An Improving Primary Decomposition of Zero-dimensional Ideals over Finite Fields An Improving Primary Decomposition of Zero-dimensional Ideals over Finite Fields

2011-12-28

arxiv.org/abs/1112.6057v3

Mathematics

Commutative Algebra

Scientific paper

This paper presents a way to improve the algorithm for computing primary decomposition of zero-dimensional ideals over finite fields given by S. Gao, D. Wan and M. Wang in 2008. Based upon the further decomposition of the invariant subspace of the Frobenius map acting on the quotient algebra in the previous algorithm, we get a more complete approach to compute all the primary components once by applying Gr\"obner basis theory. As one application of the modified approach, an improvement of Berlekamp's algorithm which computes the factorization of univariate polynomials over finite fields is also presented. Some examples given illustrate the ideas.

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