Canonical Reduction Systems in Symbolic Mathematics

  • Authors:

  • Franz Winkler

  • Affiliations:

  • RISC, Johannes Kepler University, Linz, Austria

  • Venue:
  • CAI '09 Proceedings of the 3rd International Conference on Algebraic Informatics
  • Year:
  • 2009

Quantified Score

Hi-index 0.00

Visualization

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.