A roadmap for a semi-algebraic set S is a curve which has a non-empty and connected
intersection with all connected components of S. Hence, this kind of object, introduced by …

A standard question in real algebraic geometry is to compute the number of connected
components of a real algebraic variety in affine space. This manuscript provides algorithms …

The configuration spaces of parallel manipulators exhibit more nonlinearity than serial
manipulators. Qualitatively, they can be seen to possess extra folds. Projection onto smaller …

We survey both old and new developments in the theory of algorithms in real algebraic
geometry--starting from effective quantifier elimination in the first order theory of reals due to …

We describe and analyze an algorithm for computing the homology (Betti numbers and
torsion coefficients) of basic semialgebraic sets that works in weak exponential time. That is …

We design a new algorithm for solving parametric systems of equations having finitely many
complex solutions for generic values of the parameters. More precisely, let f=(f 1,…, fm)⊂ Q …

Answering connectivity queries in semi-algebraic sets is a longstanding and challenging
computational issue with applications in robotics, in particular for the analysis of kinematic …

Let RR be a real closed field and D ⊂ RD⊂ R an ordered domain. We describe an
algorithm that given as input a polynomial P ∈ D X_ 1, ..., X_ k P∈ DX 1,…, X k and a finite …

Cuspidal robots are robots with at least two inverse kinematic solutions that can be
connected by a singularity-free path. Deciding the cuspidality of generic 3R robots has been …

We give an algorithm with singly exponential complexity for computing the barcodes up to
dimension (for any fixed) of the filtration of a given semialgebraic set by the sublevel sets of …