Chen, Changbo; Davenport, James H.; May, John P.; Moreno Maza, Marc; Xia, Bican; Xiao, Rong Triangular decomposition of semi-algebraic systems. (English) Zbl 1260.14070 J. Symb. Comput. 49, 3-26 (2013). Triangular decompositions of systems of polynomial equations produce as outputs regular chains. The paper under review introduces the notion of regular semi-algebraic systems, which should be regarded as the real (i.e., over \({\mathbb R}\)) counterpart of these regular chains. Two notions of a decomposition of a semi-algebraic system are then defined: one called lazy where the analysis of components of strictly smaller dimension is deferred, and another called full including all the cases.The authors provide running time estimates for computing these decompositions, and their implementations and experimental results are described at the end of the paper. Reviewer: Carlos D’Andrea (Barcelona) Cited in 1 ReviewCited in 14 Documents MSC: 14P10 Semialgebraic sets and related spaces 68W30 Symbolic computation and algebraic computation Keywords:regular semi-algebraic system; regular chain; lazy decomposition; triangular decomposition; border polynomial; fingerprint polynomial set Software:Maple; RegularChains PDFBibTeX XMLCite \textit{C. Chen} et al., J. Symb. Comput. 49, 3--26 (2013; Zbl 1260.14070) Full Text: DOI