Skip to main content
SpringerLink
Log in
Book cover

International Conference on Automated Deduction

CADE 1999: Automated Deduction — CADE-16 pp 112–126Cite as

VSDITLU: A Verifiable Symbolic Definite Integral Table Look-Up

Part of the Lecture Notes in Computer Science book series (LNAI,volume 1632)

Abstract

We present a verifiable symbolic definite integral table lookup: a system which matches a query, comprising a definite integral with parameters and side conditions, against an entry in a verifiable table and uses a call to a library of facts about the reals in the theorem prover PVS to aid in the transformation of the table entry into an answer. Our system is able to obtain correct answers in cases where standard techniques implemented in computer algebra systems fail. We present the full model of such a system as well as a description of our prototype implementation showing the efficacy of such a system: for example, the prototype is able to obtain correct answers in cases where computer algebra systems [CAS] do not. We extend upon Fateman’s web-based table by including parametric limits of integration and queries with side conditions.

Keywords

  • Correct Answer
  • Theorem Prove
  • Computer Algebra
  • Computer Algebra System
  • Side Condition

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

This is a preview of subscription content, access via your institution.

Chapter
USD   29.95
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (Canada)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (Canada)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. A. A. Adams, H. Gottliebsen, S. A. Linton, and U. Martin. A Verifiable Symbolic Definite Integral Table Look-Up. Technical Report CS/99/3, University of St Andrews, 1999.

    Google Scholar 

  2. E. Brinksma, editor. Tools and Algorithms for the Construction and Analysis of Systems (TACAS’ 97). Springer-Verlag LNCS 1217, 1997.

    Google Scholar 

  3. M. Bronstein. Symbolic integration I. Springer-Verlag, Berlin, 1997. Transcendental functions.

    MATH  Google Scholar 

  4. C. W. Brown. Simplification of truth-invariant cylindrical algebraic decompositions. In Gloor [Glo98], pages 295–301.

    Google Scholar 

  5. A. Bundy, editor. CADE-12: 12th International Conference on Automated Deduction: Proceedings. Springer-Verlag LNAI 814, 1994.

    Google Scholar 

  6. J. Calmet and J. A. Campbell, editors. Integrating Symbolic Mathematical Computation and Artificial Intelligence. Springer-Verlag LNCS 958, 1994.

    Google Scholar 

  7. J. Calmet and C. Limongelli, editors. Design and Implementation of Symbolic Computation Systems, International Symposium, DISCO’96. Springer-Verlag LNCS 1128, 1996.

    Google Scholar 

  8. E. Clarke and X. Zhao. Combining symbolic computation and theorem proving: Some problems of Ramanujan. In Bundy [Bun94], pages 758–763.

    Google Scholar 

  9. J. H. Davenport. Really Strong Integration Algorithms. In preparation. dB80. N. G. de Bruijn. A Survey of the Project AUTOMATH. In Seldin and Hindley [SH80], pages 579–606.

    Google Scholar 

  10. S. Dalmas, M. Gaëtano, and C. Huchet. A Deductive Database for Mathematical Formulas. In Calmet and Limongelli [CL96].

    Google Scholar 

  11. S. Dalmas, M. Gaëtano, and S. Watt. An OpenMath 1.0 Implementation. In Küchlin [Küc97], pages 241–248.

    Google Scholar 

  12. J. H. Davenport, Y. Siret, and E. Tournier. Computer algebra. Academic Press Ltd, London, second edition, 1993.

    MATH  Google Scholar 

  13. B. Dupée. Using Computer Algebra to Find Singularities of Elementary Real Functions. Available from the author, bjd@maths.bath.ac.uk, 1998.

    Google Scholar 

  14. B. Dutertre. Elements of Mathematical Analysis in PVS. In von Wright et al. [vWGH96].

    Google Scholar 

  15. T. Einwohner and R. J. Fateman. Searching techniques for Integral Tables. In Levelt [Lev95], pages 133–139.

    Google Scholar 

  16. R. J. Fateman and T. Einwohner. TILU Table of Integrals Look Up. Web Service. http://http.cs.berkeley.edu/~fateman/htest.html. 126 A. A. Adams et al.

  17. J. Fleuriot and L. Paulson. A combination of nonstandard analysis and geometry theorem proving with application to Newton’s Principia. In Kirchner and Kirchner [KK98], pages 3–16.

    Google Scholar 

  18. W. Groëbner and N. Hofreiter. Integraltafel. Springer-Verlag, Vienna, 1961.

    MATH  Google Scholar 

  19. O. Gloor, editor. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation. ACM Press, 1998.

    Google Scholar 

  20. J. Harrison. Theorem Proving with the Real Numbers. Springer-Verlag, 1998.

    Google Scholar 

  21. K. Homann and J. Calmet. Combining theorem proving and symbolic mathematical computing. In Calmet and Campbell [CC94], pages 18–29.

    Google Scholar 

  22. A. Heck. Introduction to Maple. Springer-Verlag, New York, second edition, 1996.

    MATH  Google Scholar 

  23. J. Harrison and L. Théry. Extending the HOL theorem prover with a computer algebra system to reason about the reals. In Joyce and Seger [JS94], pages 174–185.

    Google Scholar 

  24. R. D. Jenks and R. S. Sutor. AXIOM. Springer-Verlag, 1992.

    Google Scholar 

  25. J. J. Joyce and C-J. H. Seger, editors. Higher order logic theorem proving and its applications, Berlin, 1994. Springer-Verlag LNCS 780.

    MATH  Google Scholar 

  26. M. Klerer and F. Grossman. Error Rates in Tables of Indefinite Integrals. Journal of the Industrial Mathematics Society, 18:31–62, 1968.

    MathSciNet  Google Scholar 

  27. KK98. C. Kirchner and H. Kirchner, editors. CADE-15: 15th International Conference on Automated Deduction: Proceedings. Springer-Verlag LNAI 1421, 1998.

    Google Scholar 

  28. M. Kerber, M. Kohlhase, and V. Sorge. Integrating Computer Algebra with Proof Planning. In Calmet and Limongelli [CL96].

    Google Scholar 

  29. W. W. Küchlin, editor. Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation. ACM Press, 1997.

    Google Scholar 

  30. A. H. M. Levelt, editor. Proceedings of the 6th International Symposium on Symbolic and Algebraic Computation, ISSAC’ 95. Springer-Verlag LNCS 1004, 1995.

    Google Scholar 

  31. U. Martin. Computers, Reasoning and Mathematical Practice. In Computational Logic, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 1998.

    Google Scholar 

  32. S. Owre, J. Rushby, and N. Shankar. Integration in PVS: Tables, Types, and Model Checking. In Brinksma [Bri97], pages 366–383.

    Google Scholar 

  33. J. P. Seldin and J. R. Hindley, editors. To H.B. Curry: essays on combinatory logic, lambda calculus and formalism. Academic Press, 1980.

    Google Scholar 

  34. D. Stoutemyer. Crimes and misdemeanours in the computer algebra trade. Notices of the AMS, 38:779–785, 1991.

    Google Scholar 

  35. L. Théry. A Certified Version of Buchberger’s Algorithm. In Kirchner and Kirchner [KK98], pages 349–364.

    Google Scholar 

  36. A. Trybulec. The Mizar-QC 6000 logic information language. ALCC Bulletin, 6:136–140, 1978.

    Google Scholar 

  37. J. von Wright, J. Grundy, and J. Harrison, editors. Theorem Proving in Higher Order Logics: 9th International Conference. Springer-Verlag LNCS 1125, 1996.

    MATH  Google Scholar 

  38. Wolfram Research Inc. The integrator: the power to do integrals as the world has never seen before, http://www.integrals.com.

  39. D. Zwillinger, S. G. Krantz, and K. H. Rosen, editors. CRC standard mathematical tables and formulae. CRC Press, Boca Raton, FL, 30th edition, 1996.

    MATH  Google Scholar 

  40. D. Zwillinger. Standard Math Interactive. CD-ROM, 1998.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of St Andrews, St Andrews KY16 9ES, Scotland

    A. A. Adams, H. Gottliebsen, S. A. Linton & U. Martin

Authors
  1. A. A. Adams
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. H. Gottliebsen
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. S. A. Linton
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. U. Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

Copyright information

© 1999 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Adams, A.A., Gottliebsen, H., Linton, S.A., Martin, U. (1999). VSDITLU: A Verifiable Symbolic Definite Integral Table Look-Up. In: Automated Deduction — CADE-16. CADE 1999. Lecture Notes in Computer Science(), vol 1632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48660-7_8

Download citation

  • DOI: https://doi.org/10.1007/3-540-48660-7_8

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66222-8

  • Online ISBN: 978-3-540-48660-2

  • eBook Packages: Springer Book Archive

Search

Navigation