Vsditlu: A Verified Symbolic Definite Integral Table Look-Up.
Creators: name: Adams, A.A.
name: Gottliebsen, H.
name: Linton, S.A.
name: Martin, U.
Publisher: name: Zenodo
Year: 1999

description: We present a verifiable symbolic definite integral table look-up: 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. This record was migrated from the OpenDepot repository service in June, 2017 before shutting down.
description: {"references": ["[AGLM99] 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. [Bri97] E. Brinksma, editor. Tools and Algorithms for the Construction and Analysis of Systems (TACAS \u00e2\ufffd\ufffd97). Springer-Verlag LNCS 1217, 1997. [Bro97] M. Bronstein. Symbolic integration I. Springer-Verlag, Berlin, 1997. Transcendental functions. [Bro98] C. W. Brown. Simplification of truth-invariant cylindrical algebraic decompositions. In Gloor [Glo98], pages 295\u00e2\ufffd\ufffd301. [Bun94] A. Bundy, editor. CADE-12: 12th International Conference on Automated Deduction: Proceedings. Springer-Verlag LNAI 814, 1994. [CC94] J. Calmet and J. A. Campbell, editors. Integrating Symbolic Mathematical Computation and Artificial Intelligence. Springer-Verlag LNCS 958, 1994. [CL96] J. Calmet and C. Limongelli, editors. Design and Implementation of Symbolic Computation Systems, International Symposium, DISCO \u00e2\ufffd\ufffd96. Springer-Verlag LNCS 1128, 1996. [CZ94] E. Clarke and X. Zhao. Combining symbolic computation and theorem proving: Some problems of Ramanujan. In Bundy [Bun94], pages 758\u00e2\ufffd\ufffd763. [Dav] 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\u00e2\ufffd\ufffd606. [DGH96] S. Dalmas, M. Ga\ufffd\u00a8etano, and C. Huchet. A Deductive Database for Mathematical Formulas. In Calmet and Limongelli [CL96]. [DGW97] S. Dalmas, M. Ga\ufffd\u00a8etano, and S. Watt. An OpenMath 1.0 Implementation. In K\ufffd\u00a8uchlin [K\ufffd\u00a8uc97], pages 241\u00e2\ufffd\ufffd248. [DST93] J. H. Davenport, Y. Siret, and E. Tournier. Computer algebra. Academic Press Ltd, London, second edition, 1993. [Dup98] B. Dup\ufffd\u00b4ee. Using Computer Algebra to Find Singularities of Elementary Real Functions. Available from the author, bjd@maths.bath.ac.uk, 1998. [Dut96] B. Dutertre. Elements of Mathematical Analysis in PVS. In von Wright et al. [vWGH96]. [EF95] T. Einwohner and R. J. Fateman. Searching techniques for Integral Tables. In Levelt [Lev95], pages 133\u00e2\ufffd\ufffd139. [FE] R. J. Fateman and T. Einwohner. TILU Table of Integrals Look Up. Web Service. http://http.cs.berkeley.edu/fateman/htest.html. [FP98] J. Fleuriot and L. Paulson. A combination of nonstandard analysis and geometry theorem proving with application to Newton\u00e2\ufffd\ufffds Principia. In Kirchner and Kirchner [KK98], pages 3\u00e2\ufffd\ufffd16. [GH61] W. Gro\ufffd\u00a8ebner and N. Hofreiter. Integraltafel. Springer-Verlag, Vienna, 1961. [Glo98] O. Gloor, editor. Proceedings of the 1998 International Symposium on Symbolic and Algebraic Computation. ACM Press, 1998. [Har98] J. Harrison. Theorem Proving with the Real Numbers. Springer-Verlag, 1998. [HC94] K. Homann and J. Calmet. Combining theorem proving and symbolic mathematical computing. In Calmet and Campbell [CC94], pages 18\u00e2\ufffd\ufffd29. [Hec96] A. Heck. Introduction to Maple. Springer-Verlag, New York, second edition, 1996. [HT94] J. Harrison and L. Th\ufffd\u00b4ery. Extending the HOL theorem prover with a computer algebra system to reason about the reals. In Joyce and Seger [JS94], pages 174\u00e2\ufffd\ufffd185. [JS92] R. D. Jenks and R. S. Sutor. AXIOM. Springer-Verlag, 1992. [JS94] J. J. Joyce and C-J. H. Seger, editors. Higher order logic theorem proving and its applications, Berlin, 1994. Springer-Verlag LNCS 780. [KG68] M. Klerer and F. Grossman. Error Rates in Tables of Indefinite Integrals. Journal of the Industrial Mathematics Society, 18:31\u00e2\ufffd\ufffd62, 1968. [KK98] C. Kirchner and H. Kirchner, editors. CADE-15: 15th International Conference on Automated Deduction: Proceedings. Springer-Verlag LNAI 1421, 1998. [KKS96] M. Kerber, M. Kohlhase, and V. Sorge. Integrating Computer Algebra with Proof Planning. In Calmet and Limongelli [CL96]. [K\ufffd\u00a8uc97] W.W. K\ufffd\u00a8uchlin, editor. Proceedings of the 1997 International Symposium on Symbolic and Algebraic Computation. ACM Press, 1997. [Lev95] A. H. M. Levelt, editor. Proceedings of the 6th International Symposium on Symbolic and Algebraic Computation, ISSAC \u00e2\ufffd\ufffd95. Springer-Verlag LNCS 1004, 1995. [Mar98] U. Martin. Computers, Reasoning and Mathematical Practice. In Computational Logic, NATO Adv. Sci. Inst. Ser. F Comput. Systems Sci., 1998. [ORS97] S. Owre, J. Rushby, and N. Shankar. Integration in PVS: Tables, Types, and Model Checking. In Brinksma [Bri97], pages 366\u00e2\ufffd\ufffd383. [SH80] J. P. Seldin and J. R. Hindley, editors. To H.B. Curry: essays on combinatory logic, lambda calculus and formalism. Academic Press, 1980. [Sto91] D. Stoutemyer. Crimes and misdemeanours in the computer algebra trade. Notices of the AMS, 38:779\u00e2\ufffd\ufffd785, 1991. [Th\ufffd\u00b4e98] L. Th\ufffd\u00b4ery. A Certified Version of Buchberger\u00e2\ufffd\ufffds Algorithm. In Kirchner and Kirchner [KK98], pages 349\u00e2\ufffd\ufffd364. [Try78] A. Trybulec. The Mizar-QC 6000 logic information language. ALCC Bulletin, 6:136\u00e2\ufffd\ufffd 140, 1978. [vWGH96] J. von Wright, J. Grundy, and J. Harrison, editors. Theorem Proving in Higher Order Logics: 9th International Conference. Springer-Verlag LNCS 1125, 1996. [Wol] Wolfram Research Inc. The integrator: the power to do integrals as the world has never seen before, http://www.integrals.com. [ZKR96] D. Zwillinger, S. G. Krantz, and K. H. Rosen, editors. CRC standard mathematical tables and formulae. CRC Press, Boca Raton, FL, 30th edition, 1996. [Zwi98] D. Zwillinger. Standard Math Interactive. CD-ROM, 1998."]}