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This paper presents some applications of the theory of weakly nondegenerate conditions obtained by analytic methods to zero decomposition of polynomial systems and sets. Based on a known algorithm, a method is presented that can compute a strong regular series of any nonempty polynomial set. An algorithm is also devised that can decompose any polynomial system into two finite sets of strong regular sets with some good properties. In addition, we propose two alternative methods for decomposingdoi:10.1016/j.jsc.2003.10.004 fatcat:ra3zknsqezegnf27h65o7vfdyi