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A Modular Method for Computing the Splitting Field of a Polynomial

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Book cover Algorithmic Number Theory (ANTS 2006)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 4076))

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Abstract

We provide a modular method for computing the splitting field K f of an integral polynomial f by suitable use of the byproduct of computation of its Galois group G f by p-adic Stauduhar’s method. This method uses the knowledge of G f with its action on the roots of f over a p-adic number field, and it reduces the computation of K f to solving systems of linear equations modulo some powers of p and Hensel liftings. We provide a careful treatment on reducing computational difficulty. We examine the ability/practicality of the method by experiments on a real computer and study its complexity.

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Author information

Authors and Affiliations

  1. LIP6-SPIRAL, Université Paris 6, 4, place Jussieu, F-75005, Paris, France

    Guénaël Renault

  2. Department of Mathematics, Rikkyo University, 3-34-1 Nishi Ikebukuro, Toshima-ku, Tokyo, 171-8501, Japan

    Kazuhiro Yokoyama

Authors
  1. Guénaël Renault
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  2. Kazuhiro Yokoyama
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Editor information

Editors and Affiliations

  1. Technische Universität Berlin, Germany

    Florian Hess

  2. Institut für Mathematik, MA 8–1, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Sebastian Pauli

  3. Institut für Mathematik, Technische Universität Berlin, Fakultät II, MA 8-1, Strasse des 17. Juni 136, 10623, Berlin, Germany

    Michael Pohst

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© 2006 Springer-Verlag Berlin Heidelberg

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Renault, G., Yokoyama, K. (2006). A Modular Method for Computing the Splitting Field of a Polynomial. In: Hess, F., Pauli, S., Pohst, M. (eds) Algorithmic Number Theory. ANTS 2006. Lecture Notes in Computer Science, vol 4076. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11792086_10

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  • DOI: https://doi.org/10.1007/11792086_10

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-36075-9

  • Online ISBN: 978-3-540-36076-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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