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Computing roadmaps of semialgebraic sets on a variety
 Journal of the AMS
, 1997
"... 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]andSasemialgebraic subset of Z(Q), defined by a Boolean formula with atoms of the form P < 0,P> 0,P =0withP∈P, where P is a finite subset of R[X1,...,Xk]. A semialgebraic set C ..."
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Cited by 50 (17 self)
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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]andSasemialgebraic subset of Z(Q), defined by a Boolean formula with atoms of the form P < 0,P> 0,P =0withP∈P, where P is a finite subset of R[X1,...,Xk]. A semialgebraic set C is semialgebraically connected if it is nonempty and is not
On computing a set of points meeting every cell defined by a family of polynomials on a variety
 J. Complexity
, 1997
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On Computing a Set of Points meeting every Semialgebraically Connected Component of a Family of Polynomials on a Variety
 Journal of Complexity, March 1997, Vol 13, Number
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Algorithms in Semialgebraic Geometry
, 1996
"... In this thesis we present new algorithms to solve several very general problems of semialgebraic geometry. These are currently the best algorithms for solving these problems. In addition, we have proved new bounds on the topological complexity of real semialgebraic sets, in terms of the paramete ..."
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Cited by 9 (0 self)
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In this thesis we present new algorithms to solve several very general problems of semialgebraic geometry. These are currently the best algorithms for solving these problems. In addition, we have proved new bounds on the topological complexity of real semialgebraic sets, in terms of the parameters of the polynomial system defining them, which improve some old and widely used results in this field. In the first part of the thesis we describe new algorithms for solving the decision problem for the first order theory of real closed fields and the more general problem of quantifier elimination. Moreover, we prove some purely mathematical theorems on the number of connected components and on the existence of small rational points in a given semialgebraic set. The second part of this thesis deals with connectivity questions of semialgebraic sets. We develop new techniques in order to give a...