2000/05/04 by B. Bank, M. Giusti, J. Heintz +1 · 1 citation
Mathematics · #math.AG #msc:14P05 #msc:14B05 #msc:68W30
published as MSRI Preprint N0. 1999-056 · 32 pages
arxiv created 2000/05/04 · arxiv updated 2009/11/30
Let S0 be a smooth and compact real variety given by a reduced regular sequence of polynomials f1, ..., fp. This paper is devoted to the algorithmic problem of finding \em efficiently a representative point for each connected component of S0 . For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of S0. This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations f1, >..., fp and in a suitably introduced, intrinsic geometric parameter, called the \em degree of the real interpretation of the given equation system f1, >..., fp.