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Real algebraic geometry
1. Ordered Fields, Real Closed Fields.- 2. Semi-algebraic Sets.- 3. Real Algebraic Varieties.- 4. Real Algebra.- 5. The Tarski-Seidenberg Principle as a Transfer Tool.- 6. Hilbert's 17th Problem.Expand
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Algorithms in real algebraic geometry
Algebraically Closed Fields.- Real Closed Fields.- Semi-Algebraic Sets.- Algebra.- Decomposition of Semi-Algebraic Sets.- Elements of Topology.- Quantitative Semi-algebraic Geometry.- Complexity ofExpand
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On the combinatorial and algebraic complexity of quantifier elimination
TLDR
In this paper, a new algorithm for performing quantifier elimination from first order formulas over real closed fields in given. Expand
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Zeros, multiplicities, and idempotents for zero-dimensional systems
We want to propose alternative computational methods for dealing with the following three classical problems in the study of zero-dimensional systems, rephrased in the context of finite-dimensionalExpand
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Sylvester-Habicht Sequences and Fast Cauchy Index Computation
TLDR
In this paper we show how Schonhage?s strategy for computing continued fractions can be combined with the theory of sub-resultants in order to compute the Cauchy index of a rational function or the signature of a non-singular Hankel matrix in a fast and also storage efficient way. Expand
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Dynamical method in algebra: effective Nullstellensätze
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We give a general method for producing various effective Null and Positivstellensatze, and getting new Positivism in algebraically closed valued fields and ordered groups, based on dynamical proofs and simultaneous collapse. Expand
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COMPUTING ROADMAPS OF SEMI-ALGEBRAIC SETS ON A VARIETY
Let R be a real closed field, Z(Q) a real algebraic variety defined as the zero set of a polynomial Q ∈ R[X1, . . . , Xk] and S a semi-algebraic subset of Z(Q), defined by a Boolean formula withExpand
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Finding at Least One Point in Each Connected Component of a Real Algebraic Set Defined by a Single Equation
TLDR
We find, when the algebraic set is non empty, at least one point on each semi-algebraically connected component. Expand
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Sur la complexité du principe de Tarski-Seidenberg
1. I n t r o d u c t i o n Nous remercions Teresa Krick et Henri Lombardi pour l'aide qu'ils nous ont apportée et leurs nombreuses suggestions utiles concernant ce travail. Avant d'énoncer plusExpand
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