Bank, B.; Giusti, M.; Heintz, J.; Mbakop, G. M. Polar varieties and efficient real elimination. (English) Zbl 1073.14554 Math. Z. 238, No. 1, 115-144 (2001). Summary: Let \(S_0\) be a smooth and compact real variety given by a reduced regular sequence of polynomials \(f_1, \dots, f_p\). This paper is devoted to the algorithmic problem of finding efficiently a representative point for each connected component of \(S_0\). For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of \(S_0\). This leads to a procedure which solves our algorithmic problem in time that is polynomial in the (extrinsic) description length of the input equations \(f_1,\dots, f_p\) and in a suitably introduced, intrinsic geometric parameter, called the degree of the real interpretation of the given equation system \(f_1,\dots,f_p\). Cited in 1 ReviewCited in 31 Documents MSC: 14P05 Real algebraic sets 14Q99 Computational aspects in algebraic geometry 68W30 Symbolic computation and algebraic computation PDFBibTeX XMLCite \textit{B. Bank} et al., Math. Z. 238, No. 1, 115--144 (2001; Zbl 1073.14554) Full Text: DOI arXiv