On the Infrastructure of the Principal Ideal Class of an Algebraic Number Field of Unit Rank One
نویسندگان
چکیده
Let R be the regulator and let D be the absolute value of the discriminant of an order 0 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 0(RD£) for most continued fraction methods to 0(Rll2De). These ideas can also be applied to significantly decrease the number of operations needed to determine whether or not any fractional ideal of 0 is principal.
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