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 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 φ(S) ⊂ {-1,1} or dim S ≤ 2 or S is basic.
@article{urn:eudml:doc:44522,
title = {Prolongements en fonctions alg\'ebriquement constructibles.},
journal = {Revista Matem\'atica de la Universidad Complutense de Madrid},
volume = {17},
year = {2004},
pages = {471-483},
zbl = {1060.14082},
mrnumber = {MR2083966},
language = {fr},
url = {http://dml.mathdoc.fr/item/urn:eudml:doc:44522}
}
Bonnard-Doré, Isabelle. Prolongements en fonctions algébriquement constructibles.. Revista Matemática de la Universidad Complutense de Madrid, Tome 17 (2004) pp. 471-483. http://gdmltest.u-ga.fr/item/urn:eudml:doc:44522/