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Scratchpad's view of algebra I: Basic commutative 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))

Abstract

While computer algebra systems have dealt with polynomials and rational functions with integer coefficients for many years, dealing with more general constructs from commutative algebra is a more recent problem. In this paper we explain how one system solves this problem, what types and operators it is necessary to introduce and, in short, how one can construct a computational theory of commutative algebra. Of necessity, such a theory is rather different from the conventional, non-constructive, theory. It is also somewhat different from the theories of Seidenberg [1974] and his school, who are not particularly concerned with practical questions of efficiency.

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Author information

Authors and Affiliations

  1. School of Mathematical Sciences, University of Bath BA2 7AY, Claverton Down, Bath, England

    J. H. Davenport

  2. Department of Mathematical Sciences, IBM Thomas J. Watson Research Center, P.O. Box 218, 10598, Yorktown Heights, NY, USA

    B. M. Trager

Authors
  1. J. H. Davenport
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  2. B. M. Trager
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Alfonso Miola

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© 1990 Springer-Verlag Berlin Heidelberg

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Davenport, J.H., Trager, B.M. (1990). Scratchpad's view of algebra I: Basic commutative 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_122

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  • DOI: https://doi.org/10.1007/3-540-52531-9_122

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-52531-8

  • Online ISBN: 978-3-540-47014-4

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