A space efficient algorithm for group structure computation

DOI10.1090/S0025-5718-98-00968-5zbMath0965.11050OpenAlexW2013238997WikidataQ56388134 ScholiaQ56388134MaRDI QIDQ4210962

Edlyn Teske

Publication date: 10 September 1998

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

Full work available at URL: https://doi.org/10.1090/s0025-5718-98-00968-5

zbMATH Keywords

computational complexitygeneric algorithmsgroup structureideal class groupsfinite abelian groupimaginary quadratic ordersPollard's \(\rho\)-method

Mathematics Subject Classification ID

Analysis of algorithms and problem complexity (68Q25) Symbolic computation and algebraic computation (68W30) Number-theoretic algorithms; complexity (11Y16) Algebraic number theory computations (11Y40) Class numbers, class groups, discriminants (11R29) Software, source code, etc. for problems pertaining to group theory (20-04) Class groups and Picard groups of orders (11R65)

Related Items (16)

Determining the small solutions to 𝑆-unit equations ⋮ EFFICIENT ALGORITHMS FOR THE BASIS OF FINITE ABELIAN GROUPS ⋮ The distributions of individual bits in the output of multiplicative operations ⋮ Solving 𝑆-unit, Mordell, Thue, Thue–Mahler and Generalized Ramanujan–Nagell Equations via the Shimura–Taniyama Conjecture ⋮ An efficient collision detection method for computing discrete logarithms with Pollard's rho ⋮ Computing the binomial part of a polynomial ideal ⋮ On random walks for Pollard's rho method ⋮ A low-memory algorithm for finding short product representations in finite groups. ⋮ An Algorithm for Computing a Basis of a Finite Abelian Group ⋮ Linear and sublinear time algorithms for the basis of abelian groups ⋮ A generic approach to searching for Jacobians ⋮ Structure computation and discrete logarithms in finite abelian $p$-groups ⋮ Computing Hilbert class polynomials with the Chinese remainder theorem ⋮ COMPUTING NORMAL INTEGRAL BASES OF ABELIAN NUMBER FIELDS ⋮ Solving discrete logarithm problems faster with the aid of pre-computation ⋮ The Pohlig-Hellman method generalized for group structure computation

Uses Software

• LiDIA

Cites Work

• A Monte Carlo Factoring Algorithm With Linear Storage
• An improved Monte Carlo factorization algorithm
• On some computational problems in finite abelian groups
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