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Decomposing Algebraic Varieties

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Automated Deduction in Geometry (ADG 1998)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1669))

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Abstract

An algebraic variety is a geometric figure defined by the zeros of a set of multivariate polynomials. This paper explains how to adapt two general zero decomposition methods for efficient decomposition of affine algebraic varieties into unmixed and irreducible components. Two devices based on Gröbner bases are presented for computing the generators of the saturated ideals of triangular sets. We also discuss a few techniques and variants which, when properly used, may speed up the decomposition. Experiments for a set of examples are reported with comparison to show the performance and effectiveness of such techniques, variants and the whole decomposition methods. Several theoretical results are stated along with the description of algorithms. The paper ends with a brief mention of some applications of variety decomposition.

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Authors and Affiliations

  1. LEIBNIZ—IMAG—CNRS 46, avenue Félix Viallet, 38031, Grenoble Cedex, France

    Dongming Wang

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  1. Dongming Wang
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© 1999 Springer-Verlag Berlin Heidelberg

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Wang, D. (1999). Decomposing Algebraic Varieties. In: Automated Deduction in Geometry. ADG 1998. Lecture Notes in Computer Science(), vol 1669. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-47997-X_10

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  • DOI: https://doi.org/10.1007/3-540-47997-X_10

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66672-1

  • Online ISBN: 978-3-540-47997-0

  • eBook Packages: Springer Book Archive

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