We consider the problem of finding interval enclosures ot all zeros of a nonlinear system of polynomial equations. We presen~ a method which combines th e meth(g! of Grfibner: bases (used as a preprocessing step), some techniques frmn interval analysis, and a special version of the algorithm of E. Hansen for s~lving nonlinear equations in i~ne variable. The latter is applied to a tri.qngular fi)rm of the system ~d" eqnations, which is generated by. the preprocessing step: ~ Our" method is able to check if the given system has a finite mnnher of zeros and to r verifg'd enclosures for all these zeros. Several test resnhs detn~mstrate that ,our tneth~ is mpch faster than the application of Hansen's multidimensional algorithm (or similar methods) to the original nonlinear systems of polyt~nmial eqnations.
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