In this paper we present a refined version of the Newton polygon process to compute the Puiseux expansions of an algebraic function defined over the rational function field. We determine an upper bound for the bitcomplexity of computing the singular part of a Puiseux expansion by this algorithm, and use a recent quantitative version of Eisenstein’s theorem on power series expansions of algebrai...

An improved base-f expansion method is proposed, in which the bit-length of coefficients is shorter and the number of coefficients is smaller than in Kobayashi’s expansion method. The proposed method meshes well with efficient multi-exponentiation algorithms. In addition, two efficient algorithms based on the proposed expansion method, named f-wNAF and f-SJSF, are presented which significantly ...

An expression of the multivariate sigma function associated with a (n,s)-curve is given in terms of algebraic integrals. As a corollary the first term of the series expansion around the origin of the sigma function is directly proved to be the Schur function determined from the gap sequence at infinity. ∗e-mail: [email protected]

Based on the F-expansion method, and the extended version of F-expansion method, we investigate the exact solutions of the Kudryashov-Sinelshchikov equation.With the aid ofMaple, more exact solutions expressed by Jacobi elliptic function are obtained. When themodulusmof Jacobi elliptic function is driven to the limits 1 and 0, some exact solutions expressed by hyperbolic function solutions and ...

in this paper a modification of he's variational iteration method (vim) has been employed to solve dung and riccati equations. sometimes, it is not easy or even impossible, to obtain the first few iterations of vim, therefore, we suggest to approximate the integrand by using suitable expansions such as taylor or chebyshev expansions.