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MKM from Book to Computer: A Case Study

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Mathematical Knowledge Management (MKM 2003)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2594))

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Abstract

[2] is one of the great mathematical knowledge repositories. Nevertheless, it was written for a different era, and for human readership. In this paper, we describe the sorts of knowledge in one chapter (elementary transcendental functions) and the difficulties in making this sort of knowledge formal. This makes us ask questions about the nature of a Mathematical Knowledge Repository, and whether a database is enough, or whether more “intelligence” is required.

The author was partially supported by the European OpenMath Thematic Network and the Mathematical Knowledge Management Network.

The author recently had a problem with this, having set an examination question “if ∞ is algebraic and β is transcendental, is ∞β always transcendental”?One students answered in the negative, quoting the case of ∞ = 0.

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References

  1. Abbott, J. A., Díaz, A. & Sutor, R. S, OpenMath: A Protocol for the Exchange of Mathematical Information. SIGSAM Bulletin 30 (1996) 1 pp. 21–24.

    Article  Google Scholar 

  2. Abramowitz, M. & Stegun, I., Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables. US Government Printing Office, 1964. 10th Printing December 1972.

    Google Scholar 

  3. Aslaksen, H., Can your computer do complex analysis?. In: Computer Algebra Systems: A Practical Guide (M. Wester ed.), John Wiley, 1999. http://www.math.nus.edu.sg/aslaksen/helmerpub.shtml.

  4. Beeson, M. & Wiedijk, F., The Meaning of Infinity in Calculus and Computer Algebra Systems. Artificial Intelligence, Automated Reasoning, and Symbolic Computation (ed. J. Calmet et al.), Springer Lecture Notes in Artificial Intelligence 2385, Springer-Verlag, 2002, pp. 246–258.

    Google Scholar 

  5. Bradford, R. J. & Davenport, J. H., Towards Better Simplification of Elementary Functions. Proc. ISSAC 2002 (ed. T. Mora), ACM Press, New York, 2002, pp. 15–22.

    Google Scholar 

  6. Bradford, R. J., Corless, R. M., Davenport, J. H., Jeffrey, D. J. & Watt, S. M., Reasoning about the Elementary Functions of Complex Analysis. Annals of Mathematics and Artificial Intelligence36 (2002) pp. 303–318.

    Article  MathSciNet  Google Scholar 

  7. de Bruijn, N., The Mathematical Vernacular, a language for mathematics with type sets. Proc. Workshop on Programming Logic, Chalmers U., May 1987.

    Google Scholar 

  8. Corless, R. M., Davenport, J. H., Jeffrey, D. J., Litt, G. & Watt, S. M., Reasoning about the Elementary Functions of Complex Analysis. Artificial Intelligence and Symbolic Computation (ed. John A. Campbell & Eugenio Roanes-Lozano), Springer Lecture Notes in Artificial Intelligence Vol. 1930, Springer-Verlag 2001, pp. 115–126.

    Google Scholar 

  9. Corless, R. M., Davenport, J. H., Jeffrey, D. J. & Watt, S. M., “According to Abramowitz and Stegun”. SIGSAM Bulletin34 (2000) 2, pp. 58–65.

    Article  Google Scholar 

  10. Corless, R. M. & Jeffrey, D. J., The Unwinding Number. SIGSAM Bulletin 30 (1996) 2, pp. 28-35.

    Google Scholar 

  11. Davenport, J. H., Table Errata-Abramowitz & Stegun. To appear in Math. Comp.

    Google Scholar 

  12. Davenport, J. H., “According to Abramowitz and Stegun” II. OpenMath Thematic Network Deliverable ???, 2002. http://www.monet.nag.co.uk/???/

  13. Dewar, M. C., OpenMath: An Overview. ACM SIGSAM Bulletin34 (2000) 2 pp. 2–5.

    Article  Google Scholar 

  14. Kahan, W., Branch Cuts for Complex Elementary Functions. The State of Art in Numerical Analysis (ed. A. Iserles & M. J. D. Powell), Clarendon Press, Oxford, 1987, pp. 165–211.

    Google Scholar 

  15. Rich, A. D. and Jeffrey, D. J., Function evaluation on branch cuts. SIGSAM Bulletin 116(1996).

    Google Scholar 

  16. Stoutemyer, D., Crimes and Misdemeanors in the Computer Algebra Trade. Notices AMS38 (1991) pp. 779–785.

    Google Scholar 

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© 2003 Springer-Verlag Berlin Heidelberg

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Davenport, J.H. (2003). MKM from Book to Computer: A Case Study. In: Asperti, A., Buchberger, B., Davenport, J.H. (eds) Mathematical Knowledge Management. MKM 2003. Lecture Notes in Computer Science, vol 2594. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36469-2_2

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  • DOI: https://doi.org/10.1007/3-540-36469-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00568-1

  • Online ISBN: 978-3-540-36469-6

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