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>0, and counting the sum of multiplicities of the solutions in each clusters .
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>0, and counting the sum of multiplicities of the solutions in each cluster .