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Wenjun Wu's method is an algorithm for solving multivariate polynomial equations introduced in the late 1970s by the Chinese mathematician Wen-Tsun Wu. This method is based on the mathematical concept of characteristic set introduced in the late 1940s by J.F. Ritt. It is fully independent of the Gröbner basis method, introduced by Bruno Buchberger (1965), even if Gröbner bases may be used to compute characteristic sets.〔P. Aubry, D. Lazard, M. Moreno Maza (1999). On the theories of triangular sets. Journal of Symbolic Computation, 28(1–2):105–124〕 Wu's method is powerful for mechanical theorem proving in elementary geometry, and provides a complete decision process for certain classes of problem. It has been used in research in his laboratory (KLMM, Key Laboratory of Mathematics Mechanization in Chinese Academy of Science) and around the world. The main trends of research on Wu's method concern systems of polynomial equations of positive dimension and differential algebra where Ritt's results have been made effective.〔Hubert, E. ''Factorisation Free Decomposition Algorithms in Differential Algebra.'' Journal of Symbolic Computation, (May 2000): 641–662.〕〔Maple (software) package diffalg.〕 Wu's method has been applied in various scientific fields, like biology, computer vision, robot kinematics and especially automatic proofs in geometry〔Chou, Shang-Ching; Gao, Xiao Shan; Zhang, Jing Zhong. ''Machine proofs in geometry''. World Scientific, 1994.〕 ==Informal description== Wu's method uses polynomial division to solve problems of the form: : where ''f'' is a polynomial equation and ''I'' is a conjunction of polynomial equations. The algorithm is complete for such problems over the complex domain. The core idea of the algorithm is that you can divide one polynomial by another to give a remainder. Repeated division results in either the remainder vanishing (in which case the ''I'' implies ''f'' statement is true), or an irreducible remainder is left behind (in which case the statement is false). More specifically, for an ideal ''I'' in the ring ''k''() over a field ''k'', a (Ritt) characteristic set ''C'' of ''I'' is composed of a set of polynomials in ''I'', which is in triangular shape: polynomials in ''C'' have distinct main variables (see the formal definition below). Given a characteristic set ''C'' of ''I'', one can decide if a polynomial ''f'' is zero modulo ''I''. That is, the membership test is checkable for ''I'', provided a characteristic set of ''I''. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Wu's method of characteristic set」の詳細全文を読む スポンサード リンク
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