On Euclid's Algorithm and the Theory of Subresultants

  title={On Euclid's Algorithm and the Theory of Subresultants},
  author={W. S. Brown and J. Traub},
  journal={J. ACM},
Abstract : A key ingredient for systems which perform symbolic computer manipulation of multivariate rational functions are efficient algorithms for calculating polynomial greatest common divisors. Euclid's algorithm cannot be used directly because of problems with coefficient growth. The search for better methods leads naturally to the theory of subresultants. This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the subresultants of a… Expand
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The EZ GCD algorithm
  • J. Moses, D. Yun
  • Mathematics, Computer Science
  • ACM Annual Conference
  • 1973
  • 83
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  • L. Ducos
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  • RAIRO Theor. Informatics Appl.
  • 1996
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