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

Mohab Safey El Din 1, 2 Eric Schost
1 SPACES - Solving problems through algebraic computation and efficient software
INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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.
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https://hal.inria.fr/inria-00071987
Contributor : Rapport de Recherche Inria <>
Submitted on : Tuesday, May 23, 2006 - 7:25:20 PM
Last modification on : Friday, February 26, 2021 - 3:28:07 PM
Long-term archiving on: : Sunday, April 4, 2010 - 10:47:46 PM

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  • HAL Id : inria-00071987, version 1

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Mohab Safey El Din, Eric Schost. Properness defects of projections and computation of one point in each connected component of a real algebraic set. [Research Report] RR-4598, INRIA. 2002. ⟨inria-00071987⟩

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