Abstract
Based on a well-ordering principle for differential polynomial sets principles of mechanical theorem proving (MTP) and mechanical theorem discovering (MTD) are formulated and discussed. Examples are then given to show how these principles may be applied to problems in differential geometries and mechanics.
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References
Blaschke, W., Vorlesungen ueber Differential Geometrie, I. Elementare Differentialgeometrie, Auflage 3, New York (1967); II, Affine Differentialgeometrie, Auflage 2, New York (1967).
Cartan, E., Les systèmes différentiels extérieurs et leurs applications géometriques, Paris (1945).
Gabriel, J. R., SARA—A small automated reasoning assistant, Preprint, Argonne National Laboratory (1986).
Ritt, J. F., Differential Equations from the Algebraic Standpoint, Amer. Math. Soc. (1932).
Ritt, J. F., Differential Systems, Amer. Math. Soc. (1950).
Thomas, J. M., Differential Systems, Amer. Math. Soc. (1937).
Wu Wen-tsun, On the mechanization of theorem-proving in elementary and differential geometry, Scientia Sinica, Math. Supplement (I) (1979), 94–102 (in Chinese).
Wu Wen-tsun, Mechanical theorem proving in elementary geometry and differential geometry, in Proc. 1980 Beijing DD-Symposium 2 (1982), pp. 1073–1092.
WuWen-tsun, Some remarks on mechanical theorem-proving in elementary geometry, Acta Math. Scientia 3 (1983) 357–360.
WuWen-tsun, Basic principles of mechanical theorem-proving in elementary geometries, J. Systems Sci. Math. Sci. 4 (1984) 207–235. Republished in J. Automated Reasoning 2 (1986), 221–252.
Wu Wen-tsun, A constructive theory of differential algebraic geometry, in Differential Geometry & Diff. Eqs, Proceedings, Shanghai 1985, Lecture Notes in Math. No. 1255, Springer (1987), pp. 173–189.
WuWen-tsun, On zeros of algebraic equations—an application of Ritt principle, Kexue Tongbao 31 (1986), 1–5.
WuWen-tsun, A mechanization method of geometry and its applications, I. Distances, areas, and volumes, J. Systems Sci. Math. Sci. 6 (1986), 204–216.
WuWen-tsun, A mechanization method of geometry and its applications, I. Distances, areas, and volumes in euclidean and non-Euclidean geometries, Kuxue Tongbao 32 (1986), 436–440.
WuWen-tsun, A mechanization method of geometry and its applications, 2. Curve pairs of Bertrand type, Kuxue Tongbao 32 (1987) 585–588.
Wu Wen-tsun, Mechanical derivation of Newton's gravitational laws from Kepler's laws, MM-Research Preprints, No 2. (1987), pp. 53–61.
Wu Wen-tsun, Automated derivation of Newton's gravitational laws from Kepler's laws, to appear in New Trends in Automated Mathematical Reasoning (eds. A Ferro et al.).
Wu Wen-tsun, On the foundation of algebraic differential geometry, MM-Res, Preprints, No. 3 (1989), 1–26, also in Systems Sci. Math. Sci. 2 (1989), 289–312.
Wu Wen-tsun, On the generic zero and Chow basis of an irreducible ascending-set, MM-Res, Preprints, No 4 (1989).
Wu Wen-tsun, A mechanization method of equations solving and theorem proving, to appear in Issues in Robotics and Non-linear Geometry (eds. Ch. Hoffmann et al.).
Wu Wen-tsun and Wu Tianjiao, A mechanization method of geometry and its applications, 5. Solving transcendental equations by algebraic methods, MM-Res, Preprints, No. 3 (1989), 30–32.
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The present paper is partially supported by NSFC Grant JI85312.
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Wen-Tsun, W. Mechanical theorem proving of differential geometries and some of its applications in mechanics. J Autom Reasoning 7, 171–191 (1991). https://doi.org/10.1007/BF00243806
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DOI: https://doi.org/10.1007/BF00243806