English

On sign conditions over real multivariate polynomials

Algebraic Geometry 2008-12-18 v2 Computational Geometry Symbolic Computation

Abstract

We present a new probabilistic algorithm to find a finite set of points intersecting the closure of each connected component of the realization of every sign condition over a family of real polynomials defining regular hypersurfaces that intersect transversally. This enables us to show a probabilistic procedure to list all feasible sign conditions over the polynomials. In addition, we extend these results to the case of closed sign conditions over an arbitrary family of real multivariate polynomials. The complexity bounds for these procedures improve the known ones.

Keywords

Cite

@article{arxiv.0801.0586,
  title  = {On sign conditions over real multivariate polynomials},
  author = {Gabriela Jeronimo and Daniel Perrucci and Juan Sabia},
  journal= {arXiv preprint arXiv:0801.0586},
  year   = {2008}
}

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extended version

R2 v1 2026-06-21T09:59:24.360Z