Geometer: A theorem prover for algebraic geometry

  • David A. Cyrluk
  • Richard M. Harris
  • Deepak Kapur
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 310)

A Partial List of References

  1. 1.
    Buchberger, B., “Groebner Bases: An Algorithmic Method in Polynomial Ideal Theory,” in Multidimensional Systems Theory (ed. N.K. Bose), Reidel, 184–232, 1985.Google Scholar
  2. 2.
    Chou, S.C., Proving and Disproving Theorems in Elementary Geometry using Wu's Method. Ph.D. Thesis, Dept. of Mathematics, University of Texas, Austin, 1985.Google Scholar
  3. 3.
    Cyrluk, D., Kapur, D., Mundy, J., and Nguyen, V., “Formation of Partial 3D Models from 2D Projections — An Application of Algebraic Reasoning,” Proc. DARPA Workshop on Image Understanding, Los Angeles, Calif., 798–809, February 1987.Google Scholar
  4. 4.
    Kapur, D., “Using Groebner Bases to Reason about Geometry Problems,” J. of Symbolic Computation, 2, 399–408, 1986.Google Scholar
  5. 5.
    Kapur, D., “A Refutational Approach to Geometry Theorem Proving,” to appear in a special issue of the Artifical Intelligence Journal on an International Workshop on Geometry, Oxford, England, June 1986. A preliminary version appeared under the title “Geometry Theorem Proving using Hilbert's Nullstellensatz,” Proc. SYMSAC 1986, Waterloo, Canada, July 1986, 202–208.Google Scholar
  6. 6.
    Wu, W., “Basic Principles of Mechanical Theorem Proving in Elementary Geometries,” J. of System Sciences and Mathematical Sciences, 4, 3, 207–223, 1984. Also published in J. of Automated Reasoning, 2, 3, September 1986, 221–253.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1988

Authors and Affiliations

  • David A. Cyrluk
    • 1
  • Richard M. Harris
    • 2
  • Deepak Kapur
    • 3
  1. 1.Corporate Research & DevelopmentGeneral Electric Co.SchenectadyUSA
  2. 2.Dept. of Computer ScienceRensselaer Polytechnic InstituteTroyUSA
  3. 3.Dept. of Computer ScienceState University of New YorkAlbanyUSA

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