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Systems of three polynomials with two separated variables

Published: 29 July 2007 Publication History

Abstract

Motivated by the computation of intersection loci in Computer Aided Geometric Design (CAGD), we introduce and study the elimination problem for systems of three bivariate polynomial equations with separated variables. Such systems are simple sparse bivariate ones but resemble to univariate systems of two equations both geometrically and algebraically. Interesting structures for generalized Sylvester and bezoutian matrices can be explicited. Then one can take advantage of these structures to represent the objects and speed up the computations. A corresponding notion of subresultant is presented and related to a Gröbner basis of the polynomial system.

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  • (2017)Resultants and Discriminants for Bivariate Tensor-Product PolynomialsProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087646(309-316)Online publication date: 23-Jul-2017

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cover image ACM Conferences
ISSAC '07: Proceedings of the 2007 international symposium on Symbolic and algebraic computation
July 2007
406 pages
ISBN:9781595937438
DOI:10.1145/1277548
  • General Chair:
  • Dongming Wang
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Published: 29 July 2007

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Author Tags

  1. CAGD
  2. algorithms
  3. bezoutian
  4. bivariate resultants
  5. bivariate subresultant
  6. intersection problem
  7. structured matrix
  8. sylvester matrix
  9. system with separated variables

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ISSAC07
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ISSAC07: International Symposium on Symbolic and Algebraic Computation
July 29 - August 1, 2007
Ontario, Waterloo, Canada

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View all
  • (2017)Resultants and Discriminants for Bivariate Tensor-Product PolynomialsProceedings of the 2017 ACM International Symposium on Symbolic and Algebraic Computation10.1145/3087604.3087646(309-316)Online publication date: 23-Jul-2017

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