NEWTON POLYHEDRA AND ESTIMATION TO EXPONENTIAL SUMS - Atan, Kamel Arifin Mohd (Journal of ICMSA, 2006)
The classical Newton polygon is a device for computing the fractional power series expansions of algebraic functions.Â Newton gave a number of examples of this process in his âMethod of Fluxionsâ which amount to a generalÂ method. However, it was not till much later that Puiseux proved that every branch of a plane algebraic curveÂ defined by a polynomial equation f(x, y) = 0 has an expansionin a neighbourhood of a point (x0, y0) on the curve. In practice, the integers a, b and q can be read off fromÂ the Newton polygon and the coefficients cj can be determined successively with ever-increasing labour.