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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Recognizing units in number fields
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by Guoqiang Ge PDF
Math. Comp. 63 (1994), 377-387 Request permission

Abstract:

We present a deterministic polynomial-time algorithm that decides whether a power product $\prod \nolimits _{i = 1}^k {\gamma _i^{{n_i}}}$ is a unit in the ring of integers of K, where K is a number field, ${\gamma _i}$ are nonzero elements of K and ${n_i}$ are rational integers. The main algorithm is based on the factor refinement method for ideals, which might be of independent interest.
References
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Additional Information
  • © Copyright 1994 American Mathematical Society
  • Journal: Math. Comp. 63 (1994), 377-387
  • MSC: Primary 11Y40; Secondary 11R27
  • DOI: https://doi.org/10.1090/S0025-5718-1994-1242057-X
  • MathSciNet review: 1242057