Polar varieties and efficient real elimination
نویسندگان
چکیده
منابع مشابه
Polar Varieties and Efficient Real Elimination
Let S0 be a smooth and compact real variety given by a reduced regular sequence of polynomials f1, . . . , fp . This paper is devoted to the algorithmic problem of finding efficiently a representative point for each connected component of S0 . For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of S0 . This leads to a procedure which solves our al...
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Let V be a closed algebraic subvariety of the n-dimensional projective space over the com plex or real numbers and suppose that V is non-empty and equidimensional. In this paper we generalize the classic notion of polar variety of V associated with a given linear subva riety of the ambient space of V. As particular instances of this new notion of generalized polar variety we reobtain the clas...
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Let S 0 be a smooth and compact real variety given by a reduced regular sequence of polynomials f 1 ,. .. , f p. This paper is devoted to the algorithmic problem of finding efficiently a representative point for each connected component of S 0. For this purpose we exhibit explicit polynomial equations that describe the generic polar varieties of S 0. This leads to a procedure which solves our a...
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The objective of this paper is to show how the recently proposed method by Giusti, Heintz, Morais, Morgenstern, Pardo 10] can be applied to a case of real polynomial equation solving. Our main result concerns the problem of nding one representative point for each connected component of a real bounded smooth hypersurface. The algorithm in 10] yields a method for symbolically solving a zero-dimen...
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This survey covers a decade and a half of joint work with L. Lehmann, G. M. Mbakop, and L. M. Pardo. We address the problem of finding a smooth algebraic sample point for each connected component of a real algebraic variety, being only interested in components which are generically smooth locally complete intersections. The complexity of our algorithms is essentially polynomial in the degree of...
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ژورنال
عنوان ژورنال: Mathematische Zeitschrift
سال: 2001
ISSN: 0025-5874
DOI: 10.1007/pl00004896