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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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
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