Discrete Geometry for Algebraic Elimination

  • Ioannis Z. Emiris
Conference paper


Multivariate resultants provide efficient methods for eliminating variables in algebraic systems. The theory of toric (or sparse) elimination generalizes the results of the classical theory to polynomials described by their supports, thus exploiting their sparseness. This is based on a discrete geometric model of the polynomials and requires a wide range of geometric notions as well as algorithms. This survey introduces toric resultants and their matrices, and shows how they reduce system solving and variable elimination to a problem in linear algebra. We also report on some practical experience.


Matrix Polynomial Polynomial System Integer Point Mixed Volume Common Root 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Ioannis Z. Emiris
    • 1
    • 2
  1. 1.INRIA Sophia-AntipolisFrance
  2. 2.Dept. of Informatics & TelecommunicationsUniversity of AthensGreece

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