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Mathematics of Computation

ISSN 1088-6842(online) ISSN 0025-5718(print)



On the infrastructure of the principal ideal class of an algebraic number field of unit rank one

Authors: Johannes Buchmann and H. C. Williams
Journal: Math. Comp. 50 (1988), 569-579
MSC: Primary 11R11; Secondary 11R16, 11R27, 11Y16, 11Y40
MathSciNet review: 929554
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Abstract: Let R be the regulator and let D be the absolute value of the discriminant of an order $ \mathcal{O}$ of an algebraic number field of unit rank 1. It is shown how the infrastructure idea of Shanks can be used to decrease the number of binary operations needed to compute R from the best known $ O(R{D^\varepsilon })$ for most continued fraction methods to $ O({R^{1/2}}{D^\varepsilon })$. These ideas can also be applied to significantly decrease the number of operations needed to determine whether or not any fractional ideal of $ \mathcal{O}$ is principal.

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Article copyright: © Copyright 1988 American Mathematical Society

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