Description of algebraically constructible functions
Isabelle Bonnard · Advances in Geometry · 2003
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 needed to write generically a given algebraically constructible function as a sum of signs. We also prove a characterization of the polynomials appearing in a generic presentation of the function with the minimal number of polynomials. Both results are effective.