Article

Journal of Automated Reasoning

, Volume 10, Issue 2, pp 161-172

First online:

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 ChouAffiliated withDepartment of Computer Science, The Wichita State University
  • , Xiao-Shan GaoAffiliated withInstitute of Systems Science, Academia Sinica

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Abstract

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