Displaying similar documents to “Fractal dimension of sets induced by bases of imaginary quadratic fields”

Computing all monogeneous mixed dihedral quartic extensions of a quadratic field

István Gaál, Gábor Nyul (2001)

Journal de théorie des nombres de Bordeaux

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Let M be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields K with mixed signature having power integral bases and containing M as a subfield. We also determine all generators of power integral bases in K . Our algorithm combines a recent result of Kable [9] with the algorithm of Gaál, Pethö and Pohst [6], [7]. To illustrate the method we performed computations for M = ℚ ( 2 ) , ℚ ( 3 ) , ℚ ( 5 ) .