Journal of Automated Reasoning
, Volume 10, Issue 2, pp 161172
First online:
Automated reasoning in differential geometry and mechanics using the characteristic set method
 ShangChing ChouAffiliated withDepartment of Computer Science, The Wichita State University
 , XiaoShan GaoAffiliated withInstitute of Systems Science, Academia Sinica
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This is the first paper of a series of three papers under the same title. It presents an improved version of RittWu'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 Wperm, 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 Wperm RittWu's principle quasi zero set RittWu's decomposition algorithm Title
 Automated reasoning in differential geometry and mechanics using the characteristic set method
 Journal

Journal of Automated Reasoning
Volume 10, Issue 2 , pp 161172
 Cover Date
 199306
 DOI
 10.1007/BF00881834
 Print ISSN
 01687433
 Online ISSN
 15730670
 Publisher
 Kluwer Academic Publishers
 Additional Links
 Topics
 Keywords

 Differential polynomial
 weak ascending chain
 Wperm
 RittWu's principle
 quasi zero set
 RittWu's decomposition algorithm
 Industry Sectors
 Authors

 ShangChing Chou ^{(1)}
 XiaoShan Gao ^{(2)}
 Author Affiliations

 1. Department of Computer Science, The Wichita State University, 67260, Wichita, KS, USA
 2. Institute of Systems Science, Academia Sinica, 100080, Beijing, P.R. China