Local computation of differents and discriminants

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3 Citations (Scopus)

Abstract

We obtain several results on the computation of different and discriminant ideals of finite extensions of local fields. As an application, we deduce routines to compute the p-adic valuation of the discriminant Disc(f), and the resultant Res(f, g), for polynomials f(x), g(x) ∈ A[x], where A is a Dedekind domain and p is a non-zero prime ideal of A with finite residue field. These routines do not require the computation of either Disc(f) or Res(f, g); hence, they are useful in cases where this latter computation is inefficient because the polynomials have a large degree or very large coefficients. © 2013 American Mathematical Society.
Original languageEnglish
Pages (from-to)1513-1534
JournalMathematics of Computation
Volume83
Issue number287
DOIs
Publication statusPublished - 1 May 2014

Keywords

  • Different
  • Discriminant
  • Global field
  • Local field
  • Montes algorithm
  • Newton polygon
  • Okutsu invariant
  • OM representation
  • Resultant
  • Single-factor lifting algorithm

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