A New Algorithm to Find a Point in Every Cell Defined by a Family of Polynomials
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 .
KeywordsGeneral Position Positive Element Valuation Ring Complex Projective Space Common Zero
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