Newton polygon

In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields. In mathematics, the Newton polygon is a tool for understanding the behaviour of polynomials over local fields. In the original case, the local field of interest was the field of formal Laurent series in the indeterminate X, i.e. the field of fractions of the formal power series ring over K, where K was the real number or complex number field. This is still of considerable utility with respect to Puiseux expansions. The Newton polygon is an effective device for understanding the leading terms