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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.78.

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On the computation of all extensions of a $p$-adic field of a given degree
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by Sebastian Pauli and Xavier-François Roblot PDF
Math. Comp. 70 (2001), 1641-1659 Request permission


Let $\mathbf {k}$ be a $p$-adic field. It is well-known that $\mathbf {k}$ has only finitely many extensions of a given finite degree. Krasner has given formulae for the number of extensions of a given degree and discriminant. Following his work, we present an algorithm for the computation of generating polynomials for all extensions $\mathbf {K}/\mathbf {k}$ of a given degree and discriminant.
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Additional Information
  • Sebastian Pauli
  • Affiliation: Centre Interuniversitaire en Calcul Mathématique Algébrique, Concordia University, 1455 de Maisonneuve Blvd. W., Montréal, Québec, H3G 1M8, CANADA
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  • Xavier-François Roblot
  • Affiliation: Institut Girard Desargues, Université Claude Bernard (Lyon 1), 43, boulevard du 11 Novembre 1918, 69622 Villeurbanne cedex, France
  • Email:
  • Received by editor(s): May 24, 1999
  • Received by editor(s) in revised form: January 14, 2000
  • Published electronically: March 8, 2001
  • Additional Notes: The work of the first author was supported in part by ISM and FCAR/CICMA (Québec).
    The work of the second author was supported in part by NSERC (Canada) and FCAR/CICMA (Québec).
    We would like to thank David Ford for his careful reading of the original manuscript and for his useful comments.
  • © Copyright 2001 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 1641-1659
  • MSC (2000): Primary 11S15, 11S05; Secondary 11Y40
  • DOI:
  • MathSciNet review: 1836924