Univariate power series expansions in algebraic manipulation

  title={Univariate power series expansions in algebraic manipulation},
  author={Richard Zippel},
In this paper we present a complete algorithm for the determination of univariate power series expansions of meromorphic functions on a Riemann surface. The difficulties involved when expanding at singularities of various forms are discussed. We demonstrate how to use these techniques to calculate limits and as an aid in solving polynomial equations. Finally we discuss several of the implementations of power series manipulation systems with special emphasis on the implementation in MACSYMA.