Skip to main content

The design of cayley — a language for modern algebra

  • Symbolic And Algebraic Computation — Systems Design
  • Conference paper
  • First Online:
Design and Implementation of Symbolic Computation Systems (DISCO 1990)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 429))

  • 140 Accesses

Abstract

Established practice in the domain of modern algebra has shaped the design of Cayley. The design has also been responsive to the needs of its users. The requirements of the users include consistency with common mathematical notation; appropriate data types such as sets, sequences, mappings, algebraic structures and elements; efficiency; extensibility; power of in-built functions and procedures for known algorithms; and access to common examples of algebraic structures. We discuss these influences on the design of Cayley's user language.

This research was supported in part by the Australian Research Council.

Basser Department of Computer Science. Currently visiting Universität Bayreuth.

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

Access this chapter

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  • John J. Cannon, A Language for Group Theory, Department of Pure Mathematics, University of Sydney, 1982, 300 pages.

    Google Scholar 

  • John J. Cannon, An introduction to the group theory language, Cayley, Computational Group Theory, M.D. Atkinson (ed.), Academic Press, 1984, 145–183.

    Google Scholar 

  • Bruce W. Char, Keith O. Geddes, W. Morven Gentleman, Gaston H. Gonnet, The design of Maple: a compact, portable, and powerful computer algebra system, Computer Algebra, J.A. van Hulzen (ed.), Lecture Notes in Computer Science 162, Springer-Verlag, 1983, 101–115.

    Google Scholar 

  • J.H. Conway, R.T. Curtis, S.P. Norton, R.A. Parker, R.A. Wilson, Atlas of Finite Groups, Clarendon Press, Oxford, 1985.

    Google Scholar 

  • M. Hall, Jr and J.K. Senior, The Groups of Order 2 n, (n ≤ 6), Macmillan, New York, 1964.

    Google Scholar 

  • A.C. Hearn (editor), REDUCE User's Manual, version 3.2, The Rand Corporation, Santa Monica, California, April 1985.

    Google Scholar 

  • Richard D. Jenks, A primer: 11 keys to New SCRATCHPAD, EUROSAM 84, J. Fitch (ed.), Lecture Notes in Computer Science, 174, Springer-Verlag, 1984, 123–147.

    Google Scholar 

  • K. Kennedy and J. Schwartz, An introduction to the set theoretical language SETL, Comp. and Maths with Appls, 1 (1975) 97–119.

    Google Scholar 

  • M.F. Newman and E.A. O'Brien, A Cayley library for the groups of order dividing 128, submitted to Proceedings of the Singapore Group Theory Conference, June 1987.

    Google Scholar 

  • C.C. Sims, Computational methods in the study of permutation groups, Computational Problems in Abstract Algebra, J. Leech (ed.), Pergamon, Oxford, 1970, 169–183. (and unpublished manuscript)

    Google Scholar 

  • Symbolics Inc., MACSYMA Reference Manual, Version 10, Volumes 1 and 2, December 1984.

    Google Scholar 

  • N. Wirth, Programming in Modula-2, Springer-Verlag, Berlin, 1982.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Alfonso Miola

Rights and permissions

Reprints and permissions

Copyright information

© 1990 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Butler, G., Cannon, J. (1990). The design of cayley — a language for modern algebra. In: Miola, A. (eds) Design and Implementation of Symbolic Computation Systems. DISCO 1990. Lecture Notes in Computer Science, vol 429. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52531-9_119

Download citation

  • DOI: https://doi.org/10.1007/3-540-52531-9_119

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52531-8

  • Online ISBN: 978-3-540-47014-4

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics