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$% I. Bonnard-Doré, Prolongements en fonctions algébriquement constructibles, Rev. Mat. Complut. 17 (2004), 471483.%$

Prolongements en fonctions algébriquement constructibles

Isabelle BONNARD-DORÉ
Lycée Poincaré,
2 rue de la Visitation, BP 4202,
54042 Nancy Cedex France

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.