9 citations · 35 across the 6 of their papers we have counts for
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Residual ideals of MacLane valuations
Julio Fernández, Jordi Guàrdia, Jesús Montes +1
Let be a field equipped with a discrete valuation . In a pioneering work, S. MacLane determined all valuations on extending . His work was recently reviewed and ge…
Arithmetic in big number fields: the '+Ideals' package
J. Guardia, J. Montes, E. Nart
We introduce our package '+Ideals' for Magma, designed to perform the basic tasks related to ideals in number fields without pre-computing integral bases. It is based on Montes alg…
A new computational approach to ideal theory in number fields
Jordi Guardia, Jesus Montes, Enric Nart
Let be the number field determined by a monic irreducible polynomial with integer coefficients. In previous papers we parameterized the prime ideals of in terms of c…
Okutsu invariants and Newton polygons
Jordi Guardia, Jesus Montes, Enric Nart
Let K be a local field of characteristic zero, O its ring of integers and F(x) a monic irreducible polynomial with coefficients in O. K. Okutsu attached to F(x) certain primitive d…
Newton polygons and p-integral bases
Lhoussain El fadil, Jesus Montes, Enric Nart
Let p be a prime number. In this paper we use an old technique of Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by a p-r…
Higher Newton polygons and integral bases
J. Guardia, J. Montes, E. Nart
Let be a Dedekind domain, the fraction field, $\p$ a non-zero prime ideal of , and $K_\pp$ the completion of with respect to the $\p$-adic topology. At the input of…