, Volume 10, Issue 2, pp 161-172

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

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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.

The work reported here was supported in part by NSF Grants CCR-8702108 and CCR-9117870.