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

DOI:
https://doi.org/10.1090/S0025-5718-1988-0929554-6

MathSciNet review:
929554

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Abstract | References | Similar Articles | Additional Information

Abstract: Let *R* be the regulator and let *D* be the absolute value of the discriminant of an order 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 for most continued fraction methods to . These ideas can also be applied to significantly decrease the number of operations needed to determine whether or not any fractional ideal of is principal.

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DOI:
https://doi.org/10.1090/S0025-5718-1988-0929554-6

Article copyright:
© Copyright 1988
American Mathematical Society