Properness defects of projections and computation of one point in each connected component of a real algebraic set
Identifieur interne : 008308 ( Main/Exploration ); précédent : 008307; suivant : 008309Properness defects of projections and computation of one point in each connected component of a real algebraic set
Auteurs : Mohab Safey El Din ; Eric SchostSource :
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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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