(joint with Itnuit Janovitz-Freireich, Bernard Mourrain, and Lajos Ronyai)
The talk will introduce a method to compute the approximate radical of
a zero dimensional ideal which has zero clusters: the approximate radical
ideal has exactly one root in each cluster for sufficiently small clusters.
This approach is global in the sense that it eliminates all near
multiplicities simultaneously without using estimates of the roots.
The method is based on the computation of either the matrix of traces
or the Bezout matrix, both computable from the coe cients of the input
polynomial system. Asymptotic bounds are given for the accuracy of the
method in terms of the size of the clusters.