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A New Algorithm to Find a Point in Every Cell Defined by a Family of Polynomials

  • Saugata Basu
  • Richard Pollack
  • Marie-Françoise Roy
Part of the Texts and Monographs in Symbolic Computation book series (TEXTSMONOGR)

Abstract

We consider s polynomials P1,…,P s in k < s variables with coefficients in an ordered domain A contained in a real closed field R, each of degree at most d. We present a new algorithm which computes a point in each connected component of each non-empty sign condition over P1,…,P s . The output is the set of points together with the sign condition at each point. The algorithm uses s(s/k) k d O (k) arithmetic operations in A. The algorithm is nearly optimal in the sense that the size of the output can be as large as s(O(sd/k)) k .

Keywords

General Position Positive Element Valuation Ring Complex Projective Space Common Zero 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag/Wien 1998

Authors and Affiliations

  • Saugata Basu
  • Richard Pollack
  • Marie-Françoise Roy

There are no affiliations available

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