On the convergence of the multivariate ``homogeneous'' qd-algorithm (Q1347074)

The convergence theorem of the multivariate homogeneous qd-algorithm is proved exploiting an analogous theorem of the univariate theory. The homogeneous form detects polar singularities ``pointwise''. The convergence result is compared to a similar theorem for the general order multivariate qdg-algorithm, which detects the above singularities ``curvewise''.