Single-factor lifting and factorization of polynomials over local fields

DOI10.1016/j.jsc.2012.03.001zbMath1262.11106arXiv1104.3181OpenAlexW2152151784MaRDI QIDQ438687

Sebastian Pauli, Enric Nart Viñals, Jordi Guárdia i Rúbies

Publication date: 31 July 2012

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1104.3181

zbMATH Keywords

Newton polygonpolynomial factorizationMontes algorithmOkutsu invariant

Mathematics Subject Classification ID

Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Ramification and extension theory (11S15) Polynomials (11S05)

Related Items (21)

Computation of integral bases ⋮ RAMIFICATION POLYGONS, SPLITTING FIELDS, AND GALOIS GROUPS OF EISENSTEIN POLYNOMIALS ⋮ Factoring formal power series over principal ideal domains ⋮ Root repulsion and faster solving for very sparse polynomials over \(p\)-adic fields ⋮ A new computational approach to ideal theory in number fields ⋮ Super-linear convergence in the p -adic QR-algorithm ⋮ An effective description of the roots of bivariates mod pk and the related Igusa’s local zeta function ⋮ Triangular bases of integral closures ⋮ Enumerating extensions of (π)-adic fields with given invariants ⋮ Computation of triangular integral bases ⋮ Counting roots for polynomials modulo prime powers ⋮ Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields ⋮ Higher Newton polygons and integral bases ⋮ 3-torsion and conductor of genus 2 curves ⋮ Efficiently factoring polynomials modulo \(p^4\) ⋮ Local computation of differents and discriminants ⋮ On the equivalence of types ⋮ Genus computation of global function fields ⋮ Complexity of OM factorizations of polynomials over local fields ⋮ Okutsu-Montes representations of prime ideals of one-dimensional integral closures ⋮ Randomized polynomial-time root counting in prime power rings

Uses Software

• Magma
• PARI/GP

Cites Work

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• Higher Newton polygons in the computation of discriminants and prime ideal decomposition in number fields
• Construction of integral basis. I
• The construction of maximal orders over a Dedekind domain
• A fast algorithm for polynomial factorization over \(\mathbb Q_p\)
• On Hensel factorization. I
• Fast multiplication of large numbers
• 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
• Factoring polynomials over local fields.

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