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On effective computation of fundamental units. I

Authors: Michael Pohst and Hans Zassenhaus
Journal: Math. Comp. 38 (1982), 275-291
MSC: Primary 12A45; Secondary 12-04
MathSciNet review: 637307
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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 [Enhancements On Off] (What's this?)

  • [1] R. Kannan, A Polynomial Algorithm for the Two-Variable Integer Programming Problem, Report No. 78116, Institut für Ökonometrie und Operations Research, Universität Bonn.
  • [2] M. Pohst, ``Regulatorabschätzungen für total reelle algebraische Zahlkörper,'' J. Number Theory, v. 9, 1977, pp. 459-492. MR 0460274 (57:268)
  • [3] M. Pohst & H. Zassenhaus, ``An effective number geometric method of computing the fundamental units of an algebraic number field,'' Math. Comp., v. 30, 1977, pp. 754-770. MR 0498486 (58:16595)
  • [4] M. Pohst & H. Zassenhaus, ``On unit computation in real quadratic fields,'' in Symbolic and Algebraic Computation, Lecture Notes in Comput. Sci., v. 72, 1979, pp. 140-152. MR 575687 (81h:12001)
  • [5] R. Zimmert, Ideale kleiner Norm in Idealklassen und eine Regulatorabschätzung, Thesis, Bielefeld, 1978.

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Article copyright: © Copyright 1982 American Mathematical Society

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