A new computational approach to ideal theory in number fields

DOI10.1007/s10208-012-9137-5zbMath1287.11142arXiv1005.1156OpenAlexW2071102429MaRDI QIDQ385455

Jesús Montes, Enric Nart Viñals, Jordi Guárdia i Rúbies

Publication date: 2 December 2013

Published in: Foundations of Computational Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1005.1156

zbMATH Keywords

discriminantMontes algorithmideal decompositionOM representation

Mathematics Subject Classification ID

Units and factorization (11R27) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Polynomials (irreducibility, etc.) (11R09) Algebraic numbers; rings of algebraic integers (11R04) Factorization (11Y05)

Related Items (18)

Computation of integral bases ⋮ Computing with quadratic forms over number fields ⋮ The anisotropic part of a quadratic form over a number field ⋮ Square-free OM computation of global integral bases ⋮ Triangular bases of integral closures ⋮ Enumerating extensions of (π)-adic fields with given invariants ⋮ Computation of triangular integral bases ⋮ Valuations with an infinite limit-depth ⋮ Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields ⋮ Higher Newton polygons and integral bases ⋮ Local computation of differents and discriminants ⋮ On the equivalence of types ⋮ Residual ideals of MacLane valuations ⋮ Okutsu-Montes representations of prime ideals of one-dimensional integral closures ⋮ How far is an extension of \(p\)-adic fields from having a normal integral basis? ⋮ Defectless polynomials over Henselian fields and inductive valuations ⋮ Computing the Length of Sum of Squares and Pythagoras Element in a Global Field ⋮ On the discriminant of pure number fields

Uses Software

• Magma

Cites Work

• Single-factor lifting and factorization of polynomials over local fields
• Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
• Higher Newton polygons and integral bases
• Construction of integral basis. I
• Computing Riemann-Roch spaces in algebraic function fields and related topics.
• A construction for prime ideals as absolute values of an algebraic field
• Okutsu invariants and Newton polygons
• On the Complexity of the Montes Ideal Factorization Algorithm
• Factoring Polynomials over Local Fields II
• Complexity of OM factorizations of polynomials over local fields
• Newton polygons of higher order in algebraic number theory
• Local computation of differents and discriminants

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