On Computing a Set of Points Meeting Every Cell Defined by a Family of Polynomials on a Variety

@article{Basu1997OnCA,
  title={On Computing a Set of Points Meeting Every Cell Defined by a Family of Polynomials on a Variety},
  author={Saugata Basu and Richard Pollack and Marie-Françoise Roy},
  journal={J. Complex.},
  year={1997},
  volume={13},
  pages={28-37}
}
IRMAR (URA CNRS 305), Universit´e de Rennes, Campus de Beaulieu 35042 Rennes cedex, FranceReceived August 1, 1996We consider a family of s polynomials, P = f P ; ... ;P g;in k variables withcoefficients in a real closed field R; each of degree at most d; and an algebraic varietyV of real dimension k which is defined as the zero set of a polynomial Q of degreeat most d . The number of semi-algebraically connected components of all non-emptysign conditions on P over V is bounded by s ( O ( d )) . In… 
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