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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© 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
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