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On Euclid's algorithm and the computation of polynomial greatest common divisors
This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm. The phenomenon of coefficient growth is described, and the history ofExpand
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On Euclid's Algorithm and the Theory of Subresultants
TLDR
This paper presents an elementary treatment of the theory of subresultants, and examines the relationship of the sub resultants of a given pair of polynomials to their polynomial remainder sequence as determined by Euclid's algorithm. Expand
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  • PDF
Some extremal problems on r-graphs
1 . Introduction . By an r-graph we mean a fixed set of vertices together with a class of unordered subsets of this fixed set, each subset containing exactly r elements and called an r-tuple . In theExpand
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On Euclid's Algorithm and the Computation of Polynomial Greatest Common Divisors
  • W. S. Brown
  • Mathematics, Computer Science
  • JACM
  • 1 October 1971
TLDR
This paper examines the computation of polynomial greatest common divisors by various generalizations of Euclid's algorithm, with special atten- tion to the case of multivariate polynomials. Expand
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A Simple but Realistic Model of Floating-Point Computation
TLDR
A model of floating-point computation, intended as a basis for efficient portable mathematical software, is presented. Expand
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On the subresultant PRS algorithm
  • W. S. Brown
  • Mathematics, Computer Science
  • SYMSAC '76
  • 10 August 1976
TLDR
This paper is a sequel to two earlier papers [1, 2] on the generalization of Euclid's algorithm to domains of polynomials. Expand
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The Subresultant PRS Algorithm
  • W. S. Brown
  • Mathematics, Computer Science
  • TOMS
  • 1 September 1978
TLDR
Two earlier papers described the generalization of Euclid's algorithm to deal with the problem of computing the greatest common divisor (GCD) or the resultant of a pair of polynomials. Expand
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The alpak system for nonnumerical algebra on a digital computer
TLDR
This is the first of two papers on the ALPAK system for nonnumerical algebra on a digital computer. Expand
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Rational Exponential Expressions and a Conjecture Concerning π and e
One of the most controversial and least well defined of mathematical problems is the problem of simplification. The recent upsurge of interest in mechanized mathematics has lent new urgency to thisExpand
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The choice of base
TLDR
A digital computer is considered, whose memory words are composed of <italic>N</italic>. Expand
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