Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Okutsu invariants and Newton polygons   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 divisor polynomials F_1(x),..., F_r(x), that are
specially close to F(x) with respect to their degree. In this paper we
characterize the Okutsu families [F_1,..., F_r] in terms of certain Newton
polygons of higher order, and we derive some applications: closed formulas for
certain Okutsu invariants, the discovery of new Okutsu invariants, or the
construction of Montes approximations to F(x); these are monic irreducible
polynomials sufficiently close to F(x) to share all its Okutsu invariants. This
perspective widens the scope of applications of Montes' algorithm, which can be
reinterpreted as a tool to compute the Okutsu polynomials and a Montes
approximation, for each irreducible factor of a monic separable polynomial f(x)
in O[x].

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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: cond-mat
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The categories of this paper are: q-bio
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The categories of this paper are: gr-qc
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The categories of this paper are: ao-sci
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The categories of this paper are: quant-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: alg-geom
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: funct-an
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: hep-ph