Computing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets

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dc.creatorBasu, Saugata
dc.creatorPollack, Richard
dc.creatorRoy, Marie-Francoise
dc.date2006-03-10
dc.date.accessioned2026-07-07T07:06:46Z
dc.date.available2026-07-07T07:06:46Z
dc.descriptionIn this paper we describe a singly exponential algorithm for computing the first Betti number of a given semi-algebraic set. Singly exponential algorithms for computing the zero-th Betti number, and the Euler-Poincaré characteristic, were known before. No singly exponential algorithm was known for computing any of the individual Betti numbers other than the zero-th one. We also give algorithms for obtaining semi-algebraic descriptions of the semi-algebraically connected components of any given real algebraic or semi-algebraic set in single-exponential time improving on previous results.
dc.identifierhttps://arxiv.org/abs/math/0603248
dc.identifierhttp://arxiv.org/abs/math/0603248
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/110144
dc.subjectAlgebraic Geometry
dc.subjectSymbolic Computation
dc.subjectAlgebraic Topology
dc.subject14P10 ; 14P25
dc.titleComputing the First Betti Numberand Describing the Connected Components of Semi-algebraic Sets
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