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Discrete Geometry for Algebraic Elimination

In: Algebra, Geometry and Software Systems

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  • Ioannis Z. Emiris

    (INRIA Sophia-Antipolis
    University of Athens, Dept. of Informatics & Telecommunications)

Abstract

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.

Suggested Citation

  • Ioannis Z. Emiris, 2003. "Discrete Geometry for Algebraic Elimination," Springer Books, in: Michael Joswig & Nobuki Takayama (ed.), Algebra, Geometry and Software Systems, pages 77-91, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-05148-1_4
    DOI: 10.1007/978-3-662-05148-1_4
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