A Baby Step–Giant Step Roadmap Algorithm for General Algebraic Sets

@article{Basu2014ABS,
  title={A Baby Step–Giant Step Roadmap Algorithm for General Algebraic Sets},
  author={Saugata Basu and Marie-Françoise Roy and Mohab Safey El Din and {\'E}ric Schost},
  journal={Foundations of Computational Mathematics},
  year={2014},
  volume={14},
  pages={1117-1172}
}
Let $$\mathrm {R}$$R be a real closed field and $$\mathrm{D}\subset \mathrm {R}$$D⊂R an ordered domain. We present an algorithm that takes as input a polynomial $$Q \in \mathrm{D}[X_{1},\ldots ,X_{k}]$$Q∈D[X1,…,Xk] and computes a description of a roadmap of the set of zeros, $$\mathrm{Zer}(Q,\,\mathrm {R}^{k}),$$Zer(Q,Rk), of Q in $$\mathrm {R}^{k}.$$Rk. The complexity of the algorithm, measured by the number of arithmetic operations in the ordered domain $$\mathrm{D},$$D, is bounded by $$d^{O… 
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