Abstract
We investigate the application of rewrite rules to proving theorems from elementary geometry. We have proven 80 theorems, some of them quite difficult. There is a discussion of the formulation of the problem and degenerate conditions.
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References
M. Artin and W. Schelter, Graded Algebras of Global Dimension 3, Preprint (1985).
B.Buchberger, “An Algorithm Criterion for the Solvability of a System of Algebraic Equations’ (German),Aequationes Math.4 (1970), 374–383.
B. Buchberger, “Gröbner Bases: An Algorithmic Method in Polynomial Ideal Theory”, Chapter 6 inRecent Trends in Multidimensional Systems Theory, N.K. Bose (ed.) D. Reidel Publ. Comp. 1985.
S.C. Chou, “Proving Elementary Geometry Theorems Using Wu's Algorithm”, inAutomated Theorem Proving: After 25 years, Ed. By W.W. Bledsoe and D. Loveland, AMS Contemporary Mathematics Series29 (1984), 243–286.
S.C. Chou, “Proving and Discovering Theorems in Elementary Geometries Using Wu's Method”, PhD Thesis, Department of Mathematics, University of Texas, Austin (1985).
D.Hilbert,Foundations of Geometry, Open Court Publishing Company, La Salla, Illinois, 1971.
Dallas Lankford et al., “Dickson's Lemma, Hilbert's Basis Theorem, and Applications to Completion in Commutative Noetherian Rings”, preprint, Department of Mathematics and Statistics, Louisiana Tech University.
R. F.Ritt,Differential Algebra, AMS Colloquium Publications, New York, 1950.
WuWen-tsün, “On the Decision Problem and the Mechanization of Theorem Proving in Elementary Geometry”,Scientia Sinica 21 (1978) 157–179.
WuWen-tsün, “Basic Principles of Mechanical Theorem Proving in Geometries”,J. of Sys. Sci. and Math. Sci. 4 (3) (1984), 207–235.
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The authors thank the National Science Foundation for its support of the work described in this article.
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Chou, SC., Schelter, W.F. Proving geometry theorems with rewrite rules. J Autom Reasoning 2, 253–273 (1986). https://doi.org/10.1007/BF02328448
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DOI: https://doi.org/10.1007/BF02328448