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TitleComputing with semi-algebraic sets: Relaxation techniques and effective boundaries
Author(s) Changbo Chen, James H. Davenport, Marc Moreno Maza, Bican Xia, Rong Xiao
TypeArticle in Journal
AbstractWe discuss parametric polynomial systems, with algorithms for real root classification and triangular decomposition of semi-algebraic systems as our main applications. We exhibit new results in the theory of border polynomials of parametric semi-algebraic systems: in particular a geometric characterization of its “true boundary” (Definition 1). In order to optimize the corresponding decomposition algorithms, we also propose a technique, that we call relaxation, which can simplify the decomposition process and reduce the number of components in the output. This paper extends our earlier works (Chen et al., 2010, 2011).
KeywordsTriangular decomposition, Regular semi-algebraic system, Border polynomial, Effective boundary, Relaxation
URL http://www.sciencedirect.com/science/article/pii/S0747717112001307
JournalJournal of Symbolic Computation
Pages72 - 96
NoteInternational Symposium on Symbolic and Algebraic Computation
Translation No
Refereed No