Abstract
A zero decomposition algorithm is presented and used to devise a method for proving theorems automatically in differential geometry and mechanics. The method has been implemented and its practical efficiency is demonstrated by several non-trivial examples including Bertrand’s theorem, Schell’s theorem and Kepler-Newton’s laws.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Carra Ferro, G. An extension of a procedure to prove statements in differential geometry. J. Automated Reasoning 12 (1994), 351–358.
Carra Ferro, G. and Gallo, G. A procedure to prove state-ments in differential geometry. J. Automated Reasoning 6 (1990), 203–209.
Chou, S. C. and Gao, X. S. Theorems proved automatically using Wirs method - Part on differential geometry (space curves) and mechanics. MM Research Preprints 6 (1991), 37–55.
Chou, S. C. and Gao, X. S. Automated reasoning in differential geometry and mechanics using characteristic method - III. In: Automated Rea-soning (Z. Shi, ed.), pp. 1 - 12. North-Holland: Elsevier Science Publ. (1992).
Chou, S. C. and Gao, X. S. Automated reasoning in differential geometry and mechanics using the characteristic set method - I, II. J. Auto-mated Reasoning 10 (1993), 161–189.
Chou and Gao 93b] Chou, S. C. and Gao, X. S. Automated reasoning in differential geometry and mechanics using the characteristic method - IV. Syst. Sci. Math. Sci. 6 (¿993), 186–192.
Li, Z. M. Mechanical theorem proving of the local theory of surfaces. MM Research Preprints 6 (1991), 102–120.
Ritt, J. F. Differential Algebra. New York: Amer. Math. Soc. (1950).
Seidenberg, A. An elimination theory for differential algebra. Univ. California Publ. Math,. (N.S.) 3 (2) (1956), 31–66.
Wang, D. M. An elimination method for differential polynomial systems I. Preprint, LIFIA-Institut IMAG (1994).
Wang, D. M. Algebraic factoring and geometry theorem proving. In: Proc. CADE-12, Lecture Notes in Comput. Sci. 814 (1994), pp. 386–400.
Wang 95] Wang, D. M. Elimination procedures for mechanical theorem proving in geometry. Ann. Math. Artif. Intel I. (in press).
Wu, W.-T. On the mechanization of theorem-proving in elementary differential geometry (in Chinese). Sci. Sinica Special Issue on Math. (I) (1979), 94–102.
Wu, W.-T. Mechanical theorem proving in elementary geometry and elemen-tary differential geometry. In: Proc. 1980 Beijing DD-Symp., Vol. 2, pp. 1073–1092. Beijing: Science Press (1982).
Wu, W.-T. A constructive theory of differential algebraic geometry. In: Proc. 1985 Shanghai DD-SympLecture Notes in Math. 1255 (1987), pp. 173–189.
Wu, W.-T. A mechanization method of geometry and its applications - II. curve pairs of Bertrand type. Kexue Tongbao 32 (1987), 585–588.
Wu, W.-T. Mechanical derivation of Newton’s gravitational laws from Ke¬pler’s laws. MM Research Preprints 2 (1987), 53–61.
Wu, W.-T. On the foundation of algebraic differential geometry. Syst. Sci. Math. Sci. 2 (1989), 289–312.
Wu 91] Wu, W.-T. Mechanical theorem proving of differential geometries and some of its applications in mechanics. J. Automated Reasoning 7 (1991), 171–191.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1996 Springer Pub. Co.
About this chapter
Cite this chapter
Wang, D. (1996). A Method for Proving Theorems in Differential Geometry and Mechanics. In: Maurer, H., Calude, C., Salomaa, A. (eds) J.UCS The Journal of Universal Computer Science. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-80350-5_55
Download citation
DOI: https://doi.org/10.1007/978-3-642-80350-5_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-80352-9
Online ISBN: 978-3-642-80350-5
eBook Packages: Springer Book Archive