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High Quality Content by WIKIPEDIA articles! A quasi-homogeneous polynomial is a polynomial which has a degenerate Newton polygon. 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 K[[X]], over K, where K was the real number or complex number field. This is still of considerable utility with respect to Puiseux expansions.