Skip to main content

Indexes in sums and series: from formal definition to object-oriented implementation

  • Chapter
  • 114 Accesses

Part of the book series: Texts and Monographs in Symbolic Computation ((TEXTSMONOGR))

Abstract

Applicative mathematics is done with indexes. Physics, chemistry, and engineering sciences yield a wide range of applications where expressions containing indexes are used for formalizing and computing. Nevertheless, the available computer algebra systems often show little skill in dealing with expressions that contain indexes. Typical problems include: incorrect notion of variable binding and lack of knowledge about the domains over which the variables range. Wang (1990) and Cioni and Miola (1990) pointed out these deficiencies. In this paper, we show how the object-oriented design methodology proposed by the TASSO project can be applied successfully to this case.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • 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

  • Bobrow, D. G., DeMichiel, L. G., Gabriel, P., Keene, S. E., Kiczales, G., Moon, D. A. (1988): Common Lisp object system specification. Tech. Rep. X3JI3 doc. 88–002R, ANSI Common Lisp Standard Committee. (SIGPLAN Not. 23/9).

    Google Scholar 

  • Cioni, G., Miola, A. (1990): Specification and programming methodologies for axiomatizable objects manipulation: TASSO Project. Tech. Rep. P/04/31, Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Rome.

    Google Scholar 

  • Jenks, R. D., Trager, B. M. (1981): A language for computational algebra. In: Wang, P. (ed.): Proceedings ACM Symposium on Symbolic and Algebraic Manipulation, SYMSAC’81, Snowbird, Utah, USA, August 1981. Association for Computing Machinery, New York, pp. 6-13.

    Chapter  Google Scholar 

  • Limongelli, C., Temperini, M. (1992): Abstract specification of structures and methods in symbolic mathematical computation. Theor. Comput. Sci. 104: 89–107.

    Article  MathSciNet  MATH  Google Scholar 

  • Miola, A. (1983): Design specifications for manipulation of sums and series. Tech. Rep. R.66, Istituto di Analisi dei Sistemi ed Informatica, Consiglio Nazionale delle Ricerche, Rome.

    Google Scholar 

  • Shen, W., Wall, B., Wang, D. (1992): Manipulating uncertain mathematical objects: the case of indefinite sums and products. Tech. Rep. 92–23, RISC Linz, Johannes Kepler University, Linz.

    Google Scholar 

  • Wang, D. (1990): Differentiation and integration of indefinite summations. Tech. Rep. 90–37.0, RISC Linz, Johannes Kepler University, Linz.

    Google Scholar 

  • Wang, D. (1991): A toolkit for manipulating indefinite summations with application to neural networks. ACM SIGSAM Bull. 25/3: 18–27.

    Article  Google Scholar 

Download references

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer-Verlag Wien

About this chapter

Cite this chapter

Caprotti, O. (1997). Indexes in sums and series: from formal definition to object-oriented implementation. In: Miola, A., Temperini, M. (eds) Advances in the Design of Symbolic Computation Systems. Texts and Monographs in Symbolic Computation. Springer, Vienna. https://doi.org/10.1007/978-3-7091-6531-7_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-7091-6531-7_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-211-82844-1

  • Online ISBN: 978-3-7091-6531-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics