On effective computation of fundamental units. I

Pohst, Michael; Zassenhaus, Hans

doi:10.1090/S0025-5718-1982-0637307-6

On effective computation of fundamental units. I
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by Michael Pohst and Hans Zassenhaus PDF

Math. Comp. 38 (1982), 275-291 Request permission

Abstract:

The new method for efficient computation of the fundamental units of an algebraic number field developed by the authors in an earlier paper is considerably improved with respect to (Section 1) utilization to best advantage of the element of choice inherent in the method and the mastery of the linear programming techniques involved, (Section 2) ideal factorization, and (Section 3) the determination of sharper upper bounds for the index of ${U_\varepsilon }$ in ${U_F}$.

References

A Polynomial Algorithm for the Two-Variable Integer Programming Problem

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Michael Pohst and Hans Zassenhaus, An effective number geometric method of computing the fundamental units of an algebraic number field, Math. Comp. 31 (1977), no. 139, 754–770. MR 498486, DOI 10.1090/S0025-5718-1977-0498486-5
M. Pohst and H. Zassenhaus, On unit computation in real quadratic fields, Symbolic and algebraic computation (EUROSAM ’79, Internat. Sympos., Marseille, 1979) Lecture Notes in Comput. Sci., vol. 72, Springer, Berlin-New York, 1979, pp. 140–152. MR 575687

Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung