Journal of Automated Reasoning

, Volume 10, Issue 2, pp 161–172

Automated reasoning in differential geometry and mechanics using the characteristic set method

Part I. An improved version of Ritt-Wu's decomposition algorithm
  • Shang-Ching Chou
  • Xiao-Shan Gao

DOI: 10.1007/BF00881834

Cite this article as:
Chou, SC. & Gao, XS. J Autom Reasoning (1993) 10: 161. doi:10.1007/BF00881834


This is the first paper of a series of three papers under the same title. It presents an improved version of Ritt-Wu's decomposition algorithm which is the basis of our methods of mechanical theorem proving and mechanical formula derivation in differential geometry and elementary mechanics. We improve the original algorithm in two aspects. First, by using the weak ascending chain and W-perm, the sizes of the differential polynomials occurring in the decomposition can be reduced. Second, by using a special reduction procedure, the number of branches in the decomposition can be controlled effectively. The improved version significantly enhances the efficiency of the original algorithm.

Key words

Differential polynomial weak ascending chain W-perm Ritt-Wu's principle quasi zero set Ritt-Wu's decomposition algorithm 

Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • Shang-Ching Chou
    • 1
  • Xiao-Shan Gao
    • 2
  1. 1.Department of Computer ScienceThe Wichita State UniversityWichitaUSA
  2. 2.Institute of Systems ScienceAcademia SinicaBeijingP.R. China

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