Test for properness using residue calculus

We will consider global problems in the ringKX ₁, …,X _n] on the polynomials with coefficients in a subfieldK ofC. LetP=(P ₁, …,P _n):K ⁿ →K ⁿ be a polynomial map such that (P ₁,…,P _n) is a quasi-regular sequence generating a proper ideal, the main thing we do is to use the algebraic residues theory (as described in 5]) as a computational tool to give some result to test when a map (P ₁, …,P _n) is a proper map by computing a finite number of residue symbols.