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On the number of cells defined by a family of polynomials on a variety

Published online by Cambridge University Press:  26 February 2010

Saugata Basu ,
Richard Pollak  and
Marie-Françoise Roy
Saugata Basu
Affiliation:
Courant Institute of Mathematical Science, New York University, New York, NY 10012, U.S.A.
Richard Pollak
Affiliation:
Courant Institute of Mathematical Science, New York University, New York, NY 10012, U.S.A.
Marie-Françoise Roy
Affiliation:
IRMAR (URA CNRS 305), Université de Rennes, Campus de Beaulieu, 35042 Rennes cedex, France.
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Abstract

Let R be a real closed field and a variety of real dimension k′ which is the zero set of a polynomial Q∈R[X1,…, Xk] of degree at most d. Given a family of s polynomials = {P1,…, Ps}⊂R[X1,…,Xk] where each polynomial in has degree at most d, we prove that the number of cells defined by over is (O(d))k Note that the combinatorial part of the bound depends on the dimension of the variety rather than on the dimension of the ambient space.

MSC classification

Secondary: 14P10: Semialgebraic sets and related spaces
Type
Research Article
Information
Mathematika , Volume 43 , Issue 1 , June 1996 , pp. 120 - 126
Copyright
Copyright © University College London 1996

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