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On principal ideal testing in algebraic number fields

Authors
Journal
Journal of Symbolic Computation
0747-7171
Publisher
Elsevier
Publication Date
Volume
4
Issue
1
Identifiers
DOI: 10.1016/s0747-7171(87)80049-4
Disciplines
  • Computer Science
  • Mathematics

Abstract

Let F be an algebraic number field of degree n over ℚ (the rationals). An algorithm is presented for determining whether or not a given ideal in F is principal. This algorithm is applied to the problem of determining the cyclotomic numbers of order 7 for a prime p≡ 1 (mod 7). Given a 7th power non-residue of p, these numbers can be efficiently computed in O((log p) 3) binary operations.

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