Prolongements en fonctions algébriquement constructibles

Abstract

In this paper we consider the following question: Let S be a semialgebraic subset of a real algebraic set V , and let ' : S ! Z be a function on S. Is ' the restriction of an algebraically constructible function on V , i.e. a sum of signs of polynomials on V ? We give an effective method to answer this question when '(S) _ {−1, 1} or dimS _ 2 or S is basic.