# Betti numbers of semialgebraic sets defined by quantifier-free formulae

### Reference:

Gabrielov, A. and Vorobjov, N., 2005. Betti numbers of semialgebraic sets defined by quantifier-free formulae. *Discrete & Computational Geometry*, 33 (3), pp. 395-401.

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### Abstract

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).

### Details

Item Type | Articles |

Creators | Gabrielov, A.and Vorobjov, N. |

DOI | 10.1007/s00454-004-1105-7 |

Departments | Faculty of Science > Computer Science |

Refereed | Yes |

Status | Published |

ID Code | 5403 |

Additional Information | ID number: ISI:000227148900002 |

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