Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields

DOI10.5802/jtnb.782zbMath1266.11131arXiv0807.4065OpenAlexW2963254673MaRDI QIDQ449717

Jesús Montes, Enric Nart Viñals, Jordi Guárdia i Rúbies

Publication date: 31 August 2012

Published in: Journal de Théorie des Nombres de Bordeaux (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/0807.4065

zbMATH Keywords

Newton polygonsdiscriminantsideal decomposition

Mathematics Subject Classification ID

Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Polynomials (irreducibility, etc.) (11R09) Ramification and extension theory (11S15) Algebraic numbers; rings of algebraic integers (11R04) Polynomials (11S05)

Related Items (25)

Computation of integral bases ⋮ Computing with quadratic forms over number fields ⋮ Factoring formal power series over principal ideal domains ⋮ Class numbers of large degree nonabelian number fields ⋮ A new computational approach to ideal theory in number fields ⋮ The anisotropic part of a quadratic form over a number field ⋮ Super-linear convergence in the p -adic QR-algorithm ⋮ Triangular bases of integral closures ⋮ Single-factor lifting and factorization of polynomials over local fields ⋮ Lifting Artin-Schreier covers with maximal wild monodromy ⋮ Higher Newton polygons and integral bases ⋮ Newton polygons of higher order in algebraic number theory ⋮ Local computation of differents and discriminants ⋮ Discriminants of simplest \(3^n\)-tic extensions ⋮ On the equivalence of types ⋮ Genus computation of global function fields ⋮ Complexity of OM factorizations of polynomials over local fields ⋮ On the Complexity of the Montes Ideal Factorization Algorithm ⋮ Factoring Polynomials over Local Fields II ⋮ Okutsu-Montes representations of prime ideals of one-dimensional integral closures ⋮ Computation of residual polynomial operators of inductive valuations ⋮ Computing an order-complete basis for \(M^{\infty}(N)\) and applications ⋮ Computing the Length of Sum of Squares and Pythagoras Element in a Global Field ⋮ On the discriminant of pure number fields ⋮ Discriminants of Chebyshev radical extensions

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• Single-factor lifting and factorization of polynomials over local fields
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• The construction of maximal orders over a Dedekind domain
• Implementing the Round Four maximal order algorithm
• A fast algorithm for polynomial factorization over \(\mathbb Q_p\)
• Approximating rings of integers in number fields
• Okutsu invariants and Newton polygons
• On the Complexity of the Montes Ideal Factorization Algorithm
• Factoring Polynomials over Local Fields II
• Newton polygons of higher order in algebraic number theory

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