Abstract
An extension of the Carra'-Gallo procedure is presented. By using this extension, one can prove the validity of certain examples that are not within the scope of that procedure.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Buchberger, B.: Some properties of Gröbner bases for polynomial ideals,ACM SIGSAM Bull. 10 (1976), 19–21.
Carra' Ferro, G.: Gröbner Bases and Differential Algebra, inLecture Notes in Comp. Sci. 356, Springer, New York, 1987, pp. 129–140.
Carra' Ferro, G.: Some Remarks on the Differential Dimension, inLecture Notes in Comp. Sci. 357, Springer, New York, 1988, pp. 152–163.
Carra' Ferro, G. and Gallo, G.: A Procedure to Prove Geometrical Statements, inLecture Notes in Comp. Sci. 356, Springer, New York, 1987, pp. 141–150.
Carra' Ferro, G. and Gallo, G.: A procedure to prove statements in differential geometry,J. Automat. Reasoning 6 (1990), 203–209.
Cartan, E.:Les systèmes différentieles extérieurs et leuers applications géometrics, Hermann, Paris, 1945.
Chou, S. C. and Gao, X. S.: Automated reasoning in differential geometry and mechanics using the characteristic set method part I and II,J. Automat. Reasoning 10 (1993), 161–189.
Ganzha, V. G., Meleshko, S. V., and Shelest, V. P.: Application of Reduce system for analyzing consistency of systems of PDE's, inProceedings of ISSAC'90, Addison-Wesley, New York, 1990, p. 301.
Ganzha, V. G., Meleshko, S. V., and Strampp, W.: The Application of the REDUCE system to the compatibility analysis of gasdynamic equations, Preprint, 1992.
Janet, M.: Sur les systèmes d'équations aux derivées partielles,J. Math. 3 (1920), 65–151.
Kapur, D.: Using Gröbner bases to reason about geometry problems,J. Symbolic Comput. 2(4) (1986), 399–405.
Kolchin, E. R.:Differential Algebra and Algebraic Groups, Academic Press, New York, 1973.
Kuranishi, M.:Lectures on Involutive Systems of Partial Differential Equations, Publ. Soc. Math. San Paulo, 1967.
Kutzler, B. and Stifter, S.: On the application of the Buchberger's algorithm to automated geometry theorem proving,J. Symbolic Comput. 2(4) (1986), 389–398.
Pommaret, J. F.:Systems of Partial Differential Equations and Lie Pseudogroups, Gordon and Breach, New York, 1978.
Pommaret, J. F.:Differential Galois Theory, Gordon and Breach, New York, 1983.
Reid, G. J.: Algorithms for reducing a system of PDE's to standard form, determining the dimension of its solution space and calculating its Taylor series solution,European J. Appl. Math. 2 (1991), 293–318.
Riquier, C. H.:Les systèmes d'équations aux derivées partielles, Gauthier-Villars, Paris, 1910.
Ritt, J. F.:Differential Algebra, AMS Coll. Publ. 33, Amer. Math. Soc., Provident, 1950.
Schwarz, F.: An algorithm for determining the size of symmetry groups, Preprint, 1992.
Schwarz, F.: Reduction and completion algorithms for partial differential equations, inProc. ISSAC'92, preprint, 1992.
Thomas, J. M.: Riquier's existence theorems,Ann. Math. 30 (1929), 285–321.
Thomas, J. M.: Riquier's existence theorems,Ann. Math. 35 (1934), 306–311.
Wu, W. T.: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, New York, 1987.
Wu, W. T.: Mechanical theorem proving of differential geometries and some of its applications in mechanics,J. Automat. Reasoning 7(2) (1991), 171–191.
Author information
Authors and Affiliations
Additional information
Supported by Italian MURST 40%.
Rights and permissions
About this article
Cite this article
Ferro, G.C. An extension of a procedure to prove statements in differential geometry. J Autom Reasoning 12, 351–358 (1994). https://doi.org/10.1007/BF00885765
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00885765