Abstract
It is shown how the use of a certain integral basis for cyclotomic fields enables one to perform the basic operations in their ring of integers efficiently. In particular, from the representation with respect to this basis, one obtains immediately the smallest possible cyclotomic field in which a given sum of roots of unity lies. This is of particular interest when computing with the ordinary representations of a finite group.
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1980 Mathematics subject classification (1985): 11R, 11Y
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Bosma, W. Canonical bases for cyclotomic fields. AAECC 1, 125–134 (1990). https://doi.org/10.1007/BF01810296
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DOI: https://doi.org/10.1007/BF01810296