An algorithm for the principal ideal problem in indefinite quaternion algebras

Aurel Page 1, 2
2 LFANT - Lithe and fast algorithmic number theory
IMB - Institut de Mathématiques de Bordeaux, Inria Bordeaux - Sud-Ouest
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.
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  • HAL Id : hal-00996346, version 1
  • ARXIV : 1405.6674

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Aurel Page. An algorithm for the principal ideal problem in indefinite quaternion algebras. Algorithmic Number Theory Symposium ANTS XI, Aug 2014, GyeongJu, South Korea. pp.366-384. ⟨hal-00996346⟩

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