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On the algebraic formulation of certain geometry statements and mechanical geometry theorem proving |
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| Authors: | Shang -Ching Chou and Jin -Gen Yang |
| Affiliation: | (1) Institute for Computing Science, The University of Texas at Austin, 78712 Austin, TX, USA;(2) Department of Mathematics, University of Texas at Austin, 78712 Austin, TX, USA |
| Abstract: | In this paper we analyze the algebraic formulations of certain geometry statements appearing in recent literature related to mechanical geometry theorem proving and give several examples to show that one of these formulations can cause serious problems. We clarify a formulation which is essentially due to W. T. Wu and, in our opinion, is the most satisfactory.This author was supported by NSF Grants DCR-8503498 and CCR-8702108. |
| Keywords: | Geometry theorem proving Provers Nondegenerate conditions Ritt's algorithms Wu's method The Grö bner basis method Algebraically (or real) closed field Algebraic geometry Irreducible variety Nondegenerate component Generally true Simson's theorem Pappus' theorem |
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