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Transactions of the American Mathematical Society

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Conjugacy problem in $ {\rm GL}\sb 2({\bf Z}[\sqrt{-1}])$ and units of quadratic extensions of $ {\bf Q}(\sqrt{-1})$

Author: Hironori Onishi
Journal: Trans. Amer. Math. Soc. 293 (1986), 83-98
MSC: Primary 11R27; Secondary 11F75, 20G30
MathSciNet review: 814914
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Abstract: A highly efficient procedure for deciding if two given elements of $ {\text{G}}{{\text{L}}_2}(\mathbf{Z}[\sqrt { - 1} ])$ are conjugate or not will be presented. It makes use of a continued fraction algorithm in $ \mathbf{Z}[\sqrt { - 1} ]$ and gives a fundamental unit of any given quadratic extension of $ \mathbf{Q}(\sqrt { - 1} )$.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1986 American Mathematical Society

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