Full paper in PDF:
$% I. Bonnard-Doré, Prolongements en fonctions algébriquement constructibles, Rev. Mat. Complut. 17 (2004), 471–483.%$

Prolongements en fonctions algébriquement constructibles

Isabelle BONNARD-DORÉ
Lycée Poincaré,
2 rue de la Visitation, BP 4202,
54042 Nancy Cedex — France
isabelle.bonnard@laposte.net

Received: April 7, 2003
Accepted: May 5, 2004
ABSTRACT

In this paper we consider the following question: Let S be a semialgebraic subset of a real algebraic set V , and let f :S-- > Z be a function on S . Is f 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 f(S) < {-1,1} or dimS < 2 or S is basic.

Key words: semialgebraic sets, algebraically constructible functions, quadratic forms.
2000 Mathematics Subject Classification: 14P10.