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arXiv · 1405.6674

An algorithm for the principal ideal problem in indefinite quaternion algebras

Aurel Page
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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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Aurel Page. 2014-05-26. An algorithm for the principal ideal problem in indefinite quaternion algebras. https://doi.org/10.1112/s1461157014000321

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