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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.[1][2]
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.[3][4] Wu's method has been applied in various scientific fields, like biology, computer vision, robot kinematics and especially automatic proofs in geometry.[5]
- ^ Corrochano, Eduardo Bayro; Sobczyk, Garret, eds. (2001). Geometric algebra with applications in science and engineering. Boston, Mass: Birkhäuser. p. 110. ISBN 9780817641993.
- ^ P. Aubry, D. Lazard, M. Moreno Maza (1999). On the theories of triangular sets. Journal of Symbolic Computation, 28(1–2):105–124
- ^ Hubert, E. Factorisation Free Decomposition Algorithms in Differential Algebra. Journal of Symbolic Computation, (May 2000): 641–662.
- ^ Maple (software) package diffalg.
- ^ Chou, Shang-Ching; Gao, Xiao Shan; Zhang, Jing Zhong. Machine proofs in geometry. World Scientific, 1994.