Newton polygons of higher order in algebraic number theory

By Jordi Guàrdia, Jesús Montes, Enric Nart. 2008

154 citations recorded by the source corpus.

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 the irreducible factors. This carries out a program suggested by . Ore. As an application, we obtain fast algorithms to compute discriminants, prime ideal decomposition and integral bases of number elds.

Subfields: Computational Theory and Mathematics, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/6237073a862870847b3e816ad29fb758f2334b4d

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In Computational Theory and Mathematics

1. Jesús Montes
2. Enric Nart
3. Jordi Guàrdia
4. Lhoussain El Fadil

In Geometry and Topology

1. Jesús Montes
2. Enric Nart
3. Jordi Guàrdia
4. Lhoussain El Fadil

Citations in the corpus

• NEWTON POLYGONS AND p-INTEGRAL BASES OF QUARTIC NUMBER FIELDS (2012, methodology): “[3]).”
• Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields (2008, methodology): “This algorithm is obtained by a direct application of the ideas of [7].”