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On efficient computation of the 2-parts of ideal class groups of quadratic fields. (English) Zbl 1078.11063

The authors use a fast algorithm for computing the 2-part of the class group in the narrow sense of a quadratic number field from W. Bosma and P. Stevenhagen [J. Théor. Nombres Bordx. 8, 283-313 (1986; Zbl 0870.11080)]. They combine it with a relation between ternary quadratic forms and ideals. Thus they can also calculate the 2-part of the usual class group very fast.

MSC:

11R29 Class numbers, class groups, discriminants
11R11 Quadratic extensions
11Y40 Algebraic number theory computations
11E20 General ternary and quaternary quadratic forms; forms of more than two variables

Citations:

Zbl 0870.11080
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References:

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