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Journal Articles Discrete and Computational Geometry Year : 2004

Properness defects of projections and computation of at least one point in each connected component of a real algebraic set

Abstract

Computing at least one point in each connected component of a real algebraic set is a basic subroutine to decide emptiness of semi-algbraic sets, which is a fundamental algorithmic problem in effective real algebraic geometry. In this article, we propose a new algorithm for this task, which avoids a hypothesis of properness required in many of the previous methods. We show how studying the set of non-properness of a linear projection enables to detect connected components of a real algebraic set without critical points. Our algorithm is based on this result and its practical counterpoint, using the triangular representation of algebraic varieties. Our experiments show its efficiency on a family of examples.

Dates and versions

inria-00099962 , version 1 (26-09-2006)

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Mohab Safey El Din, Eric Schost. Properness defects of projections and computation of at least one point in each connected component of a real algebraic set. Discrete and Computational Geometry, 2004, 32 (3), pp.417-430. ⟨10.1007/s00454-004-1107-5⟩. ⟨inria-00099962⟩
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