Polar varieties and computation of one point in each connected component of a smooth real algebraic set
Identifieur interne : 007492 ( Main/Exploration ); précédent : 007491; suivant : 007493Polar varieties and computation of one point in each connected component of a smooth real algebraic set
Auteurs : Mohab Safey El Din ; Eric SchostSource :
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Abstract
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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