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Automated Reasoning and Equation Solving with the Characteristic Set Method

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Abstract

A brief introduction to the characteristic set method is given for solving algebraic equation systems and then the method is extended to algebraic difference systems. The method can be used to decompose the zero set for a difference polynomial set in general form to the union of difference polynomial sets in triangular form. Based on the characteristic set method, a decision procedure for the first order theory over an algebraically closed field and a procedure to prove certain difference identities are proposed.

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Authors and Affiliations

  1. Key Laboratory of Mathematics Mechanization, Institute of Systems Science, AMSS, Chinese Academy of Sciences, Beijing, 100080, P.R. China

    Wen-Tsun Wu & Xiao-Shan Gao

Authors
  1. Wen-Tsun Wu
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  2. Xiao-Shan Gao
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Correspondence to Wen-Tsun Wu.

Additional information

Regular Paper: This work is supported by the National Grand Fundamental Research 973 Program of China under Grant No. 2004CB318000.

Wen-Tsun Wu is a professor at the Academy of Mathematics and Systems Sciences, Chinese Academy of Sciences and a member of Chinese Academy of Sciences. In the 1950s, Wu discovered the Wu class and Wu formulas in topology. In the late 1970s, Prof. Wu invented a method of automated geometry theorem proving, known as Wu’s method, and a method of solving algebraic and differential equations, known as Ritt-Wu’s zero decomposition theorem. He was a recipient of the Herbrand Award for Distinguished Contributions to Automated Reasoning in 1997, the National Supreme Award of Science and Technology of China in 2000, and the Shaw Prize in Mathematical Sciences 2006.

Xiao-Shan Gao is a professor and the director of the Institute of Systems Science, Chinese Academy of Sciences. His research interests include: automated reasoning, symbolic computation, intelligent CAD, CAGD, and robotics. He has published over one hundred research papers. Webpage: http://www.mmrc.iss.ac.cn/∼xgao.

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Wu, WT., Gao, XS. Automated Reasoning and Equation Solving with the Characteristic Set Method. J Comput Sci Technol 21, 756–764 (2006). https://doi.org/10.1007/s11390-006-0756-7

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  • DOI: https://doi.org/10.1007/s11390-006-0756-7

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