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Communication Dans Un Congrès Année : 2003

Polar varieties and computation of one point in each connected component of a smooth real algebraic set

Résumé

Let $f_1, \ldots, f_s$ be polynomials in $\Q[X_1, \ldots, X_n]$ that generate a radical ideal and let $V$ be their complex zero-set. Suppose that $V$ is smooth and equidimensional; then we show that computing suitable sections of the polar varieties associated to generic projections of $V$ gives at least one point in each connected component of $V\cap\R^n$. We deduce an algorithm that extends that of Bank, Giusti, Heintz and Mbakop to non-compact situations. Its arithmetic complexity is polynomial in the complexity of evaluation of the input system, an intrinsic algebraic quantity and a combinatorial quantity.
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Dates et versions

inria-00099649 , version 1 (26-09-2006)

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Citer

Mohab Safey El Din, Eric Schost. Polar varieties and computation of one point in each connected component of a smooth real algebraic set. International Symposium on Symbolic and Algebraic Computation 2003 - ISSAC'2003, Aug 2003, Philadelphie, PA, United States. pp.224-231, ⟨10.1145/860854.860901⟩. ⟨inria-00099649⟩
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