论文信息 - On Principal Ideal Testing in Algebraic Number Fields

On Principal Ideal Testing in Algebraic Number Fields

Let F be an algebraic number field of degree n over @? (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.

Johannes A. Buchmann | Hugh C. Williams | J. Buchmann | H. Williams

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