The complexity of computing all subfields of an algebraic number field

DOI10.1016/j.jsc.2018.06.001zbMath1419.11143arXiv1606.01140OpenAlexW2962962711WikidataQ129655446 ScholiaQ129655446MaRDI QIDQ1733310

Jonas Szutkoski, Mark van Hoeij

Publication date: 21 March 2019

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

Full work available at URL: https://arxiv.org/abs/1606.01140

zbMATH Keywords

latticepartitionssubfields

Mathematics Subject Classification ID

Symbolic computation and algebraic computation (68W30) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40)

Related Items (3)

Factorization and root-finding for polynomials over division quaternion algebras ⋮ Identifying central endomorphisms of an abelian variety via Frobenius endomorphisms ⋮ Ring extensions of length two

Uses Software

• Magma
• PARI/GP

Cites Work

• Isomorphisms of algebraic number fields
• Computing congruences efficiently
• Factoring polynomials with rational coefficients
• On computing subfields. A detailed description of the algorithm
• The Magma algebra system. I: The user language
• Generating subfields
• Gradual sub-lattice reduction and a new complexity for factoring polynomials
• A relative van Hoeij algorithm over number fields
• Powers of tensors and fast matrix multiplication
• A polynomial reduction algorithm
• Symmetric Functions, m-Sets, and Galois Groups
• Sharp estimates for triangular sets
• Block Systems of a Galois Group
• Meet and join within the lattice of set partitions
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