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Kamel Arifin Mohd Atan
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Mathematics

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NEWTON POLYHEDRA AND ESTIMATION TO EXPONENTIAL SUMS Kamel Arifin Mohd Atan
Proceedings of ICMSA Vol 2, No 1 (2006): Pure Maths : ICMSA 2006
Publisher : Proceedings of ICMSA

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Abstract

The classical Newton polygon is a device for computing the fractional power series expansions of algebraic functions. Newton gave a number of examples of this process in his ”Method of Fluxions” which amount to a general method. However, it was not till much later that Puiseux proved that every branch of a plane algebraic curve 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 from the Newton polygon and the coefficients cj can be determined successively with ever-increasing labour.
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