Exploració per autor "Montes Peral, Jesús"

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    • A new computational approach to ideal theory in number fields 

      Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric (2013)
      Article
      Accés obert
      Let K be the number field determined by a monic irreducible polynomial f(x) with integer coefficients. In previous papers we parameterized the prime ideals of K in terms of certain invariants attached to Newton polygons ...

    • Higher Newton polygons and integral bases 

      Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric (2015)
      Article
      Accés obert
      Let A be a Dedekind domain whose field of fractions K is a global field. Let p be a non-zero prime ideal of A, and Kp the completion of K atp. The Montes algorithm factorizes a monic irreducible separable polynomial f(x) ...

    • Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields 

      Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric (2011-12-01)
      Article
      Accés obert
      We present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a p-adic factorization method based on Newton polygons of higher order. The running-time ...

    • Newton polygons of higher order in algebraic number theory 

      Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric (2012-01-10)
      Article
      Accés obert
      We develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a p-adic eld, together with relevant arithmetic information about the elds generated by ...

    • Residual ideals of MacLane valuations 

      Fernández González, Julio; Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric (2015)
      Article
      Accés obert
      Let K be a field equipped with a discrete valuation v. In a pioneering work, MacLane determined all valuations on K(x) extending v. His work was recently reviewed and generalized by Vaqui´e, by using the graded algebra ...