Conjugacy problem in 𝐺𝐿₂(𝑍[√-1]) and units of quadratic extensions of 𝑄(√-1)

Onishi, Hironori

doi:10.1090/S0002-9947-1986-0814914-9

Conjugacy problem in $\textrm {GL}_ 2(\textbf {Z}[\sqrt {-1}])$ and units of quadratic extensions of $\textbf {Q}(\sqrt {-1})$
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Trans. Amer. Math. Soc. 293 (1986), 83-98 Request permission

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

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