Now showing items 1-5 of 5

  • A new computational approach to ideal theory in number fields 

    Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric (2013)
    Article
    Open Access
    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
    Open Access
    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
    Open Access
    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
    Open Access
    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
    Open Access
    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 ...