An effective implementation of symbolic–numeric cylindrical algebraic decomposition for quantifier elimination

With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic–numeric cylindrical algebraic decomposit...

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Bibliographic Details
Published in:	Theoretical computer science Vol. 479; pp. 43 - 69
Main Authors:	Iwane, Hidenao, Yanami, Hitoshi, Anai, Hirokazu, Yokoyama, Kazuhiro
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.04.2013
Subjects:	Cylindrical algebraic decomposition Quantifier elimination Symbolic–numeric computation Quantifier elimination Cylindrical algebraic decomposition Symbolic–numeric computation
ISSN:	0304-3975, 1879-2294
Online Access:	Get full text
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Summary:	With many applications in engineering and scientific fields, quantifier elimination (QE) has received increasing attention. Cylindrical algebraic decomposition (CAD) is used as a basis for a general QE algorithm. In this paper we present an effective symbolic–numeric cylindrical algebraic decomposition (SNCAD) algorithm for QE incorporating several new devices, which we call “quick tests”. The simple quick tests are run beforehand to detect an unnecessary procedure that might be skipped without violating the correctness of results and they thus considerably reduce the computing time. The effectiveness of the SNCAD algorithm is examined in a number of experiments including practical engineering problems, which also reveal the quality of the implementation. Experimental results show that our implementation has significantly improved efficiency compared with our previous work.
ISSN:	0304-3975 1879-2294
DOI:	10.1016/j.tcs.2012.10.020