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Ritt-Wu's decomposition algorithm and geometry theorem proving

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10th International Conference on Automated Deduction (CADE 1990)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 449))

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Abstract

An improved Ritt-Wu's decomposition (of an algebraic set into the union of irreducible varieties) algorithm is given. The algorithm has been used to prove geometric theorems that Wu's original method addresses. Unlike Wu's original approach, nondegenerate conditions are given explicitly at the beginning, not generated during the proof process. A program based on this improved version of the algorithm proved more than 500 theorems, including Morley's trisector theorem.

The work reported here was supported in part by the NSF Grant CCR-8702108.

On leave from Institute of Systems Science, Academia Sinica, Beijing.

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References

  1. S.C. Chou, “Proving Elementary Geometry Theorems Using Wu's Algorithm”, in Automated Theorem Proving: After 25 years, Ed. By W.W. Bledsoe and D. Loveland, AMS Contemporary Mathematics Series 29 (1984), 243–286.

    Google Scholar 

  2. S.C. Chou, “Proving and Discovering Theorems in Elementary Geometries Using Wu's Method”, PhD Thesis, Department of Mathematics, University of Texas, Austin (1985).

    Google Scholar 

  3. S.C. Chou, Mechanical Geometry Theorem Proving, D. Reidel Publishing Company, Dordrecht, Netherlands, 1988.

    Google Scholar 

  4. S. C. Chou and X. S. Gao, “Ritt-Wu's Decomposition Algorithm and Geometry Theorem Proving”, Technical Report 89-09, Department of Computer Sciences, University of Texas at Austin, 1989.

    Google Scholar 

  5. S.C. Chou and X.S. Gao, “A Class of Geometry Statements of Constructive Type and Geometry Theorem Proving”, TR-89-37, Computer Sciences Department, The University of Texas at Austin, November, 1989.

    Google Scholar 

  6. S.C. Chou and X.S. Gao, “Techniques for Ritt-Wu's Decomposition Algorithm”, TR-90-2, Computer Sciences Department, The University of Texas at Austin, February, 1990.

    Google Scholar 

  7. S.C. Chou and W.F. Schelter, “Proving Geometry Theorems with Rewrite Rules”, Journal of Automated Reasoning, 2(4) (1986), 253–273.

    Google Scholar 

  8. R. Hartshorne, Algebraic Geometry, Sprigner-Verlag, 1978.

    Google Scholar 

  9. D. Kapur, “Geometry Theorem Proving Using Hilbert's Nullstellensatz”, in Proceedings of the 1986 Symposium on Symbolic and Algebraic Computation, 202–208.

    Google Scholar 

  10. D. Kapur and J. Mundy, “Wu's Method and its Application to Perspective Viewing”, Artificial Intelligence Journal, V. 37 (1988), pp.15–36.

    Google Scholar 

  11. D. Kapur and Hoi K. Wan, “Refutational Proofs of Geometry Theorems via Characteristic Sets”, to appear in ISSAC'90.

    Google Scholar 

  12. H.P. Ko and S.C. Chou, “Polynomial Triangulation for Pseudo Common Divisors”, Technical Report, 85CRD242, General Electric Company, 1985.

    Google Scholar 

  13. H.P. Ko, “Geometry Theorem Proving by Decomposition of Quasi-Algebraic Sets: An Application of the Ritt-Wu Principle”, Artificial Intelligence, Vol. 37, pp95–122 (1988).

    Google Scholar 

  14. J. F. Ritt, Differential Algebra, AMS Colloquium Publications, New York, 1950.

    Google Scholar 

  15. Hoi Wan, “On proving Geometry Theorems via Characteristic Set Computation”, MS Project Report, Department of Computer Science, RPI, Troy, Dec., 1987.

    Google Scholar 

  16. Wu Wen-tsün, “On the Decision Problem and the Mechanization of Theorem Proving in Elementary Geometry”, Scientia Sinica 21 (1978), 157–179.

    Google Scholar 

  17. Wu Wen-tsün, “Basic Principles of Mechanical Theorem Proving in Geometries”, J. of Sys. Sci. and Math. Sci. 4(3), 1984, 207–235, republished in Journal of Automated Reasoning 2(4) (1986), 221–252.

    Google Scholar 

  18. Wu Wen-tsün, “On Zeros of Algebraic Equations — An Application of Ritt's Principle”, Kexue Tongbao 31(1) (1986), 1–5.

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Sciences, The University of Texas at Austin, 78712, Austin, Texas, USA

    Shang-Ching Chou & Xiao-Shan Gao

Authors
  1. Shang-Ching Chou
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  2. Xiao-Shan Gao
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Mark E. Stickel

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© 1990 Springer-Verlag Berlin Heidelberg

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Chou, SC., Gao, XS. (1990). Ritt-Wu's decomposition algorithm and geometry theorem proving. In: Stickel, M.E. (eds) 10th International Conference on Automated Deduction. CADE 1990. Lecture Notes in Computer Science, vol 449. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52885-7_89

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  • DOI: https://doi.org/10.1007/3-540-52885-7_89

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52885-2

  • Online ISBN: 978-3-540-47171-4

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