Abstract
Let n be a fixed natural number, fεZ[x] a monic irreducible polynomial of degree n. Let F=Q(ρ) be the algebraic number field which is generated by a root ρ of f and assume that 1, ρ, ρ 2, ..., ρ n−1 is a Z-basis of the maximal order O of F. In this paper we describe an algorithm by which the class group Cl of F can be computed in D 1+ε binary operations where D denotes the discriminant of F.
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© 1989 Springer-Verlag Berlin Heidelberg
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Buchmann, J., Pohst, M. (1989). On the complexity of computing class groups of algebraic number fields. In: Mora, T. (eds) Applied Algebra, Algebraic Algorithms and Error-Correcting Codes. AAECC 1988. Lecture Notes in Computer Science, vol 357. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51083-4_53
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DOI: https://doi.org/10.1007/3-540-51083-4_53
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