Cylindrical algebraic decomposition using local projections. (September 2016)

• Record Type: Journal Article
• Authors: Strzeboński, Adam
• Is Part Of: Journal of symbolic computation. Volume 76(2016)
• Page Start: 36
• Page End: 64
• Publication Date: 2016-09
• Subjects: Semialgebraic sets -- Cylindrical algebraic decomposition -- Solving inequalities -- Quantifier elimination; Mathematics -- Data processing -- Periodicals; Numerical analysis -- Data processing -- Periodicals; Automatic programming (Computer science) -- Periodicals; Mathématiques -- Informatique -- Périodiques; Analyse numérique -- Informatique -- Périodiques; Programmation automatique -- Périodiques; Automatic programming (Computer science); Mathematics -- Data processing; Numerical analysis -- Data processing; Periodicals; Electronic journals; 510.285
• DOI: 10.1016/j.jsc.2015.11.018
• Languages: English
• ISSNs: 0747-7171

Abstract

Abstract: We present an algorithm which computes a cylindrical algebraic decomposition of a semialgebraic set using projection sets computed for each cell separately. Such local projection sets can be significantly smaller than the global projection set used by the Cylindrical Algebraic Decomposition (CAD) algorithm. This leads to reduction in the number of cells the algorithm needs to construct. A restricted version of the algorithm was introduced inStrzeboński (2014) . The full version presented here can be applied to quantified formulas and makes use of equational constraints. We give an empirical comparison of our algorithm and the classical CAD algorithm.