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Polynomial real root isolation using approximate arithmetic
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Computing a 3-dimensional cell in an arrangement of quadrics: exactly and actually!
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A Singly-Expenential Stratification Scheme for Real Semi-Algebraic Varieties and Its Applications
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Efficient isolation of polynomial's real roots
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Intersecting quadrics: an efficient and exact implementation
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An exact and efficient approach for computing a cell in an arrangement of quadrics
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Intersecting quadrics: an efficient and exact implementation
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In this paper, we study a sweeping algorithm for computing the arrangement of a set of quadrics in R^3. We define a ''trapezoidal'' decomposition in the sweeping plane, and we study the evolution of this subdivision during the sweep. A key point of this algorithm is the manipulation of algebraic numbers. In this perspective, we put a large emphasis on the use of algebraic tools, needed to compute the arrangement, including Sturm sequences and Rational Univariate Representation of the roots of a multivariate polynomial system.