2014/01/01 by A. Page, Aurel Page · 3 citations
Computer Science · Mathematics · #Algebra over a field #Cryptography and Residue Arithmetic #Field (mathematics) #Generator (circuit theory) #Ideal (ethics) #Numerical Methods and Algorithms #Polynomial and algebraic computation #Principal (computer security) #Quaternion #math.NT
paper · pdf · doi:10.1112/s1461157014000321
published in LMS Journal of Computation and Mathematics 17(A), 366-384 (London Mathematical Society) · To appear in ANTS XI
openalex publication_date 2014/01/01 · arxiv created 2014/05/26 · arxiv updated 2014/08/13 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
Abstract Deciding whether an ideal of a number field is principal and finding a generator is a fundamental problem with many applications in computational number theory. For indefinite quaternion algebras, the decision problem reduces to that in the underlying number field. Finding a generator is hard, and we present a heuristically subexponential algorithm.