Torical modification of Newton non-degenerate ideals

We give a definition of Newton non-degeneracy independent of the system of generators defining the variety. This definition extends the notion of Newton non-degeneracy to varieties that are not necessarily complete intersection. As in the previous definition of non-degeneracy for complete intersection varieties, it is shown that the varieties satisfying our definition can be resolved with a toric modification. Using tools of both toric and tropical geometry we describe the toric modification in terms of the Grobner fan of the ideal defining the variety. The first part of the paper is devoted to introducing the classical concepts and the proof for the hypersurface case.