Exploració per autor "Nart Vinyals, Enric"

Ara es mostren els items 1-8 de 8

    • 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 ...

    • Genetics of polynomials over local fields 

      Guàrdia Rubies, Jordi; Nart Vinyals, Enric (2015)
      Article
      Accés obert
      Let (K, v) be a discrete valued field with valuation ring O, and let Ov be the completion of O with respect to the v-adic topology. In this paper we discuss the advantages of manipulating polynomials in Ov[x] on a computer ...

    • 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) ...

    • Of limit key polynomials 

      Alberich Carramiñana, Maria; Fernández Boix, Albert.; Fernández González, Julio; Guàrdia Rubies, Jordi; Nart Vinyals, Enric; Roé Vellvé, Joaquim (2021-04-01)
      Article
      Accés obert
      Let ν be a valuation of arbitrary rank on the polynomial ring K[x] with coefficients in a field K. We prove comparison theorems between MacLane-Vaquié key polynomials for valuations μ ≤ν and abstract key polynomials for ...

    • 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 ...

    • Square-free OM computation of global integral bases 

      Guàrdia Rubies, Jordi; Nart Vinyals, Enric (2022-09-27)
      Article
      Accés obert
      For a prime p, the OM algorithm finds the p-adic factorization of an irreducible polynomial f¿Z[x]¿¿Z[¿] in polynomial time. This may be applied to construct p-integral bases in the number field K defined by f. In this ...

    • Valuations with an infinite limit-depth 

      Alberich Carramiñana, Maria; Guàrdia Rubies, Jordi; Nart Vinyals, Enric; Roé Vallvé, Joaquim (2023-08-08)
      Article
      Accés restringit per política de l'editorial
      We construct a field K and a valuation-algebraic valuation on K[x] , whose underlying Maclane–Vaquié chain consists of an infinite (countable) number of limit augmentations.

    • Valuative trees over valued fields 

      Alberich Carramiñana, Maria; Guàrdia Rubies, Jordi; Nart Vinyals, Enric; Roé Vallvé, Joaquim (Elsevier, 2023-01-15)
      Article
      Accés obert
      For an arbitrary valued field (K, v) and a given extension v(K*) ¿¿ ¿ of ordered groups, we analyze the structure of the tree formed by all ¿-valued extensions of v to the polynomial ring K[x]. As an application, we find ...