Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case - Sorbonne Université Access content directly
Journal Articles Computers & Mathematics with Applications Year : 2010

Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case

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 pth root of any element in the field product. Experiments with a preliminary implementation show the effectiveness of our algorithms.

Dates and versions

hal-00706787 , version 1 (11-06-2012)

Identifiers

Cite

Xiaoliang Li, Chenqi Mou, Dongming Wang. Decomposing polynomial sets into simple sets over finite fields: The zero-dimensional case. Computers & Mathematics with Applications, 2010, 60 (11), pp.2983-2997. ⟨10.1016/j.camwa.2010.09.059⟩. ⟨hal-00706787⟩
139 View
0 Download

Altmetric

Share

Gmail Facebook X LinkedIn More