Journal of Automated Reasoning

, Volume 6, Issue 2, pp 203–209 | Cite as

A procedure to prove statements in differential geometry

  • Giuseppa Carrà Ferro
  • Giovanni Gallo
Article

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.

Key words

Differential algebraic set differential dimension 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Cassidy, P. J., ‘Differential algebraic groups’, Am. J. Math. 14, 891–954 (1972).Google Scholar
  2. 2.
    Carrà Ferro, G., ‘Gröbner bases and differential algebra’, Proceeding AAECC-5 (1987) Lecture Notes in Comp. Sci. 356, 129–140 (1989).Google Scholar
  3. 3.
    Carrà Ferro, G., ‘Some remark on the differential dimension’, Proceeding AAECC-6 (1988) Lecture Notes in Comp. Sci. 357, 152–163.Google Scholar
  4. 4.
    Carrà Ferro, G. and Gallo, G., ‘A procedure to prove geometrical statements’, Proceeding AAECC-5 (1987) Lecture Notes in Comp. Sci. 356, 141–150.Google Scholar
  5. 5.
    Chou, S. C., ‘Proving and discovering geometry theorems using Wu's method’, PhD Thesis. Univ. of Texas at Austin (1985).Google Scholar
  6. 6.
    Kapur, D., ‘Using Gröbner bases to reason about geometry problems’, J. Symb. Comp. 2, 4 399–405 (1986).Google Scholar
  7. 7.
    Kolchin, E. R., Differential Algebra and Algebraic Groups, Academic Press, New York (1973).Google Scholar
  8. 8.
    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).Google Scholar
  9. 9.
    Ritt, J. F., ‘Differential algebra’, AMS Colloq. Public., vol. 33, New York (1950).Google Scholar
  10. 10.
    Winkler, F., ‘A geometrical decision algorithm based on the Gröbner bases algorithm’, submitted to ISSAC-88.Google Scholar
  11. 11.
    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).Google Scholar
  12. 12.
    Wu Wen Tsün, ‘Automatic derivation of Newton's gravitational laws from Kepler's laws’, Preprint (1987).Google Scholar

Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Giuseppa Carrà Ferro
    • 1
  • Giovanni Gallo
    • 1
  1. 1.Dipartimento di MatematicaUniversità di CataniaCataniaItaly

Personalised recommendations