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Series Expansions of Algebraic Functions

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Computational Algebra and Number Theory

Part of the book series: Mathematics and Its Applications ((MAIA,volume 325))

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Abstract

Algebraic functions over Q(X) may indeed be expressed as Puiseux series. We examine an algorithm for the development of the series expansion for algebraic functions. From the algorithm we show why the series developed over fields of finite characteristic will not necessarily be Puiseux.

The series y = 1 + X 1/2 + X 3/4 + X 7/8 + ... satisfies y 2 + Xy + 1+ X = 0 over F 2. The shape of such series, which satisfy algebraic functions but which are not Puiseux series, is explored.

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References

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Author information

Authors and Affiliations

  1. School of Mathematics & Statistics, University of Sydney, NSW, 2006, Australia

    Deryn Griffiths

Authors
  1. Deryn Griffiths
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Editor information

Editors and Affiliations

  1. School of Mathematics and Statistics, University of Sydney, Sydney, Australia

    Wieb Bosma

  2. CeNTRe for Number Theory Research, Macquarie University, Sydney, Australia

    Alf van der Poorten

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© 1995 Springer Science+Business Media Dordrecht

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Griffiths, D. (1995). Series Expansions of Algebraic Functions. In: Bosma, W., van der Poorten, A. (eds) Computational Algebra and Number Theory. Mathematics and Its Applications, vol 325. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-1108-1_19

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  • DOI: https://doi.org/10.1007/978-94-017-1108-1_19

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-90-481-4560-7

  • Online ISBN: 978-94-017-1108-1

  • eBook Packages: Springer Book Archive

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