Article ID Journal Published Year Pages File Type
469084 Computers & Mathematics with Applications 2010 15 Pages PDF
Abstract

This paper presents algorithms for decomposing any zero-dimensional polynomial set into simple sets over an arbitrary finite field, with an associated ideal or zero decomposition. As a key ingredient of these algorithms, we generalize the squarefree decomposition approach for univariate polynomials over a finite field to that over the field product determined by a simple set. As a subprocedure of the generalized squarefree decomposition approach, a method is proposed to extract the ppth root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms.

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