Triangular decomposition of semi-algebraic systems

被引：29

作者：

Chen, Changbo ^{[1
]}

Davenport, James H. ^{[2
]}

May, John P. ^{[3
]}

Maza, Marc Moreno ^{[1
]}

Xia, Bican ^{[4
]}

Xiao, Rong ^{[1
,4
]}

机构：

[1] Univ Western Ontario, London, ON N6A 5B7, Canada

[2] Univ Bath, Bath BA2 7AY, Avon, England

[3] Maplesoft, Waterloo, ON N2V 1K8, Canada

[4] Peking Univ, Beijing 100871, Peoples R China

来源：

JOURNAL OF SYMBOLIC COMPUTATION | 2013年 / 49卷

基金：

加拿大自然科学与工程研究理事会;

关键词：

Regular semi-algebraic system; Regular chain; Lazy decomposition; Triangular decomposition; Border polynomial; Fingerprint polynomial set;

D O I：

10.1016/j.jsc.2011.12.014

中图分类号：

TP301 [理论、方法];

学科分类号：

081202 ;

摘要：

Regular chains and triangular decompositions are fundamental and well-developed tools for describing the complex solutions of polynomial systems. This paper proposes adaptations of these tools focusing on solutions of the real analogue: semi-algebraic systems. We show that any such system can be decomposed into finitely many regular semi-algebraic systems. We propose two specifications (full and lazy) of such a decomposition and present corresponding algorithms. Under some simplifying assumptions, the lazy decomposition can be computed in singly exponential time w.r.t. the number of variables. We have implemented our algorithms and present experimental results illustrating their effectiveness. (C) 2011 Elsevier Ltd. All rights reserved.

引用

页码：3 / 26

页数：24

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