Some remarks concerning the complexity of computing class groups of quadratic fields (Q1179460)
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scientific article; zbMATH DE number 24659
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Some remarks concerning the complexity of computing class groups of quadratic fields |
scientific article; zbMATH DE number 24659 |
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Some remarks concerning the complexity of computing class groups of quadratic fields (English)
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26 June 1992
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The authors obtain several results concerning the complexity of computations in quadratic number fields \(F\). Under the assumption of the generalized Riemann hypothesis they prove among other things that the following problems are in \(NP\cap \hbox{co-}NP\) for every order \(\mathcal O\) of \(F\): (i) Is a given ideal \(A\) of \(\mathcal O\) principal? (ii) Do given ideals \(A_ 1,\dots,A_ k\) of \(\mathcal O\) generate the class group?
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class group computations
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complexity
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quadratic number fields
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