Abstract
An algorithm for theorem proving in differential geometry based on the calculation of the differential dimension of differential quasi-algebraic sets is shown. In the case in which only ordinary differential equations are involved, an algorithm for such computation is presented. Different notions of validity for differential geometry statements are also compared.
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References
Cassidy, P. J., ‘Differential algebraic groups’, Am. J. Math. 14, 891–954 (1972).
Carrà Ferro, G., ‘Gröbner bases and differential algebra’, Proceeding AAECC-5 (1987) Lecture Notes in Comp. Sci. 356, 129–140 (1989).
Carrà Ferro, G., ‘Some remark on the differential dimension’, Proceeding AAECC-6 (1988) Lecture Notes in Comp. Sci. 357, 152–163.
Carrà Ferro, G. and Gallo, G., ‘A procedure to prove geometrical statements’, Proceeding AAECC-5 (1987) Lecture Notes in Comp. Sci. 356, 141–150.
Chou, S. C., ‘Proving and discovering geometry theorems using Wu's method’, PhD Thesis. Univ. of Texas at Austin (1985).
Kapur, D., ‘Using Gröbner bases to reason about geometry problems’, J. Symb. Comp. 2, 4 399–405 (1986).
Kolchin, E. R., Differential Algebra and Algebraic Groups, Academic Press, New York (1973).
Kutzler, B. and Stifter, S., ‘On the application of Buchberger's algorithm to automated geometry theorem proving’, J. Symb. Comp. 2, 4, 389–398 (1986).
Ritt, J. F., ‘Differential algebra’, AMS Colloq. Public., vol. 33, New York (1950).
Winkler, F., ‘A geometrical decision algorithm based on the Gröbner bases algorithm’, submitted to ISSAC-88.
Wu Wen Tsün, ‘A constructive theory of differential algebraic geometry based on works of J. F. Ritt with particular applications to mechanical theorem proving of differential geometries’, Lecture Notes in Math. 1255, Springer-Verlag (1987).
Wu Wen Tsün, ‘Automatic derivation of Newton's gravitational laws from Kepler's laws’, Preprint (1987).
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This paper was supported by Italian M.P.I. (40% 1985).
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Ferro, G.C., Gallo, G. A procedure to prove statements in differential geometry. J Autom Reasoning 6, 203–209 (1990). https://doi.org/10.1007/BF00245819
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DOI: https://doi.org/10.1007/BF00245819