Newton non-degenerate polynomial ideals

Kouchnirenko in 1976 shows a formula to compute the Milnor number of isolated singularity germs of functions in terms of the Newton polyhedron of the germ. Bivia-Ausina, Fukui and Saia in 2002 characerized a class of finite codimension ideals in the ring of formal power series which satisfy a Newton non degeneracy condition, moreover they showed how to compute the Hilbert Samuel multiplicity of such ideals in term of a convenient Newton polyhedron. On the other side Kouchnirenko shows a formula to compute the Milnor number of Newton non degenerate polinomilas in terms of its Newton polyhedron. The main purppose of this project is to develop a study about the Newton non degeneracy condition for ideals in the ring of polinomial functions C[x] and methods to compute the multiplicity in terms of convenient Newton polyhedra. We shall also develope this study to the class of Laurent polynomials, following the ideas of Kouchnirenko.