@inproceedings{886129e0dd4e440485544116c8054a1a,
title = "Decomposing algebraic varieties",
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 Gr{\"o}bner 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.",
author = "Dongming Wang",
note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 1999.; 2nd International Workshop on Automated Deduction in Geometry, ADG 1998 ; Conference date: 01-08-1998 Through 03-08-1998",
year = "1999",
doi = "10.1007/3-540-47997-x\_10",
language = "英语",
isbn = "3540666729",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "180--206",
editor = "Xiao-Shan Gao and Dongming Wang and Lu Yang",
booktitle = "Automated Deduction in Geometry - 2nd International Workshop, ADG 1998, Proceedings",
address = "德国",
}