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Decomposing algebraic varieties

  • CNRS

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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.

Original languageEnglish
Title of host publicationAutomated Deduction in Geometry - 2nd International Workshop, ADG 1998, Proceedings
EditorsXiao-Shan Gao, Dongming Wang, Lu Yang
PublisherSpringer Verlag
Pages180-206
Number of pages27
ISBN (Print)3540666729, 9783540666721
DOIs
StatePublished - 1999
Externally publishedYes
Event2nd International Workshop on Automated Deduction in Geometry, ADG 1998 - Beijing, China
Duration: 1 Aug 19983 Aug 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume1669
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference2nd International Workshop on Automated Deduction in Geometry, ADG 1998
Country/TerritoryChina
CityBeijing
Period1/08/983/08/98

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