论文信息 - Newton polygons of higher order in algebraic number theory

Newton polygons of higher order in algebraic number theory

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.

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