Before revision:  We introduce the local solution clustering problem for a system of polynomial equations, that is grouping all its complex solutions lying in an initial complex domain in clusters smaller than a given real number \epsilon^n, for any given \epsilon} > 0, and counting the sum of multiplicities of the solutions in each cluster. For triangular systems, we propose a criterion based on the Pellet theorem to count the sum of the multiplicities of the solutions in a cluster. We also propose an algorithm for solving the local solution clustering problem for triangular systems, based on a recent near-optimal algorithm  for clustering the complex roots of univariate polynomials .
After revision:  We introduce the local solution clustering problem for a system of polynomial equations, that is grouping all its complex solutions lying in an initial complex domain in clusters smaller than a given real number \epsilon^n, for any given \epsilon} > 0. Our algorithm is based on a recent near-optimal algorithm for clustering the complex roots of univariate polynomials .