The Comparison Between Wu Method And Gr(?)bner Basis Method And Some Applications

Starting with analyzing the feature and essential difference between a Ritt-characteristic set, a Wu-characteristic set and a Grobner basis from both a theoretic and algorithmic viewpoint, this dissertation clarifies, by means of the pseudo-division algorithm, the in-trinsic connection between a Ritt-characteristic set, a Wu-characteristic set and a Grobner basis. As a result, a feasible algorithm for computing a Ritt-characteristic set by using a reduced Grobner basis (under the lexicographic ordering) is obtained, and a criterion for checking whether the achieved Ritt-characteristic set is a Wu-characteristic set is realized by using only a simple division procedure.