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An algorithm for the principal ideal problem in indefinite quaternion algebras

Part of: Computational number theory Algebraic number theory: global fields

Published online by Cambridge University Press:  01 August 2014

A. Page
A. Page*
Affiliation:
Université Bordeaux, IMB UMR 5251, F-33400 Talence, France email [email protected] CNRS, IMB, UMR 5251, F-33400 Talence, France INRIA, F-33400 Talence, France

Abstract

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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.

MSC classification

Secondary: 11Y40: Algebraic number theory computations 11R52: Quaternion and other division algebras 11R65: Class groups and Picard groups of orders
Type
Research Article
Information
LMS Journal of Computation and Mathematics , Volume 17 , Special Issue A: Algorithmic Number Theory Symposium XI , 2014 , pp. 366 - 384
Copyright
© The Author 2014 

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