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International Conference on Algebraic Informatics

CAI 2009: Algebraic Informatics pp 123–135Cite as

Canonical Reduction Systems in Symbolic Mathematics

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5725))

Abstract

Many algorithmic methods in mathematics can be seen as constructing canonical reduction systems for deciding membership problems. Important examples are the Gauss elimination method for linear systems, Euclid’s algorithm for computing greatest common divisors, Buchberger’s algorithm for constructing Gröbner bases, or the Knuth-Bendix procedure for equational theories. We explain the basic concept of a canonical reduction system and investigate the close connections between these algorithms.

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References

  1. Avenhaus, J.: Reduktionssysteme. Springer, Heidelberg (1995)

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  2. Book, R.V., Otto, R.: String-Rewriting Systems. Springer, Heidelberg (1993)

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  3. Knuth, D.E., Bendix, P.B.: Simple Word Problems in Universal Algebra. In: Leech, J. (ed.) Computational Problems in Abstract Algebra, pp. 263–297. Pergamon Press, Oxford (1970)

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  4. Winkler, F.: The Church–Rosser property in computer algebra and special theorem proving: An investigation of critical–pair/completion algorithms, Dissertation Univ. Linz, Austria, VWGÖ Wien (1984)

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  5. Winkler, F.: Polynomial Algorithms in Computer Algebra. Springer, Wien New York (1996)

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Author information

Authors and Affiliations

  1. RISC, Johannes Kepler University, Linz, Austria

    Franz Winkler

Authors
  1. Franz Winkler
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Editor information

Editors and Affiliations

  1. Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    Symeon Bozapalidis

  2. Department of Mathematics, Aristotle University of Thessaloniki, 54124, Thessaloniki, Greece

    George Rahonis

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© 2009 Springer-Verlag Berlin Heidelberg

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Winkler, F. (2009). Canonical Reduction Systems in Symbolic Mathematics. In: Bozapalidis, S., Rahonis, G. (eds) Algebraic Informatics. CAI 2009. Lecture Notes in Computer Science, vol 5725. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03564-7_7

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  • DOI: https://doi.org/10.1007/978-3-642-03564-7_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03563-0

  • Online ISBN: 978-3-642-03564-7

  • eBook Packages: Computer ScienceComputer Science (R0)

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