Algebraic statistics exploits the use of algebraic techniques to develop new paradigms and
algorithms for data analysis. The development of computational algebra software provides a …

Algebraically constructible functions on a real algebraic set are sums of signs of polynomials
on this set. The representation theorem gives an effective criterion to characterize these …

Abstract top We present a characterization of sums of signs of global analytic functions on a
real analytic manifold M of dimension two. Unlike the algebraic case, obstructions at infinity …

The algebraically constructible functions on a real algebraic set are the sums of signs of
polynomials on this set. We prove a formula giving the minimal number of polynomials …

Semialgebraic sets are rather ubiquitous in mathematics and nature. The reason is that
since they are described by polynomials on one hand they are “easy” to manipulate and on …

[AcAnBg], one sees that different kind of obstructions can appear. Some are of lo cal nature
in the sense that they are concentrated at a point, like in Figure 1 below, where A and B …

Abstract top In this paper we consider the following question: Let S be a semialgebraic
subset of a real algebraic set V, and let φ: S→ Z be a function on S. Is φ the restriction of an …

Soit V⊂ RN un ensemble algébrique réel.(Les ensembles algébriques considérés ici seront
toujours des sous-ensembles algébriques d'un espace affine.) On note P (V) et R (V) …