Browsing by Author "Montes Peral, Jesús"

A new computational approach to ideal theory in number fields
Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart Vinyals, Enric (2013)
Article
Open AccessLet 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 AccessLet A be a Dedekind domain whose field of fractions K is a global field. Let p be a nonzero 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 (20111201)
Article
Open AccessWe present an algorithm for computing discriminants and prime ideal decomposition in number fields. The algorithm is a refinement of a padic factorization method based on Newton polygons of higher order. The runningtime ... 
Newton polygons of higher order in algebraic number theory
Guàrdia Rubies, Jordi; Montes Peral, Jesús; Nart, Enric (20120110)
Article
Open AccessWe develop a theory of arithmetic Newton polygons of higher order, that provides the factorization of a separable polynomial over a padic 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 AccessLet 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 ...