Betti numbers of semialgebraic sets defined by quantifier-free formulae

A Gabrielov, N Vorobjov

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Let X be a semialgebraic set in R-n defined by a Boolean combination of atomic formulae of the kind h * 0 where * is an element of { >, greater than or equal to, = }, deg(h) < d, and the number of distinct polynomials h is k. We prove that the sum of Betti numbers of X is less than O(k(2)d)(n).
Original languageEnglish
Pages (from-to)395-401
Number of pages7
JournalDiscrete & Computational Geometry
Issue number3
Publication statusPublished - 2005


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