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A description is given of a modified version of Voronoi's algorithm for ob- taining the regulator of a pure cubic field (2(\A>)- This new algorithm has the ad- vantage of executing relatively rapidly for large values of D. It also eliminates a com- putational problem which occurs in almost all algorithms for finding units in algebraic number fields. This is the problem of performing calculations involving algebraic ir- rationals by using only approximations of these numbers. The algorithm was implemented on a computer and run on all values of D (< 10 ) such that the class number of Q_(\Jd) is not divisible by 3. Several tables summarizing the results of this computation are also presented.

Calculation of the regulator of a pure cubic field