Multidimensional residues and complexity problems Original Research Article

Our main objective in this note is to show how multidimensional residues can be used to make explicit division formulas in polynomial algebras; we will also discuss division problems with Laurent polynomials and detail, in some particular cases, the methods that can be used to compute the complete sum of residues of a rational function; we will finally indicate the relation between the search of effective bounds and the numerical computation of multidimensional integrals.