Fernández González, JulioGuàrdia, JordiMontes, JesúsNart, Enric2020-06-162020-06-162015-040021-8693https://hdl.handle.net/2445/165873Let $K$ be a field equipped with a discrete valuation $v$. In a pioneering work, S. MacLane determined all extensions of $v$ to discrete valuations on $K(x)$. His work was recently reviewed and generalized by M. Vaquié, by using the graded algebra of a valuation. We extend Vaquié's approach by studying residual ideals of the graded algebra of a valuation as an abstract counterpart of certain residual polynomials which play a key role in the computational applications of the theory. As a consequence, we determine the structure of the graded algebra of any discrete valuation on $K(x)$ and we show how these valuations may be used to parameterize irreducible polynomials over local fields up to Okutsu equivalence.46 p.application/pdfeng(c) Elsevier, 2015ÀlgebraAritmètica computacionalAlgebraComputer arithmeticinfo:eu-repo/semantics/article6458232020-06-16info:eu-repo/semantics/openAccess