论文信息 - Some remarks concerning the complexity of computing class groups of quadratic fields

Some remarks concerning the complexity of computing class groups of quadratic fields

Abstract Let O be an order of any quadratic number field. In this paper we show that under the assumption of the generalized Riemann hypothesis the following decision problems are in NP ⊃ co-NP: 1. 1. Is a given ideal A of O principal? 2. 2. Given ideals A 1 , … , Aκ of O , do their equivalence classes generate the class group of O ? 3. 3. Given ideals A 1 , … , Aκ of O , is the class group of O the direct product of the cyclic subgroups generated by the equivalence classes of the A 1 ?

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

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