Computing all monogeneous mixed dihedral quartic extensions of a quadratic field
Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, p. 137-142

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=(2),(3),(5).

Soit M un corps quadratique réel. Nous donnons un algorithme rapide pour déterminer tous les corps quartiques diédraux K avec signature mixte, monogènes (i.e. ayant des bases d’entiers 1,α,α 2 ,α 3 ) et contenant M comme sous-corps. Nous déterminons également tous les générateurs α des bases dans K ayant cette forme. Notre algorithme combine un résultat récent de Kable [9] avec l’algorithme de Gaál, de Pethö et de Pohst [6], [7]. On applique la méthode à M=(2),(3),(5).

@article{JTNB_2001__13_1_137_0,
     author = {Ga\'al, Istv\'an and Nyul, G\'abor},
     title = {Computing all monogeneous mixed dihedral quartic extensions of a quadratic field},
     journal = {Journal de th\'eorie des nombres de Bordeaux},
     publisher = {Universit\'e Bordeaux I},
     volume = {13},
     number = {1},
     year = {2001},
     pages = {137-142},
     zbl = {1065.11086},
     mrnumber = {1838076},
     language = {en},
     url = {http://www.numdam.org/item/JTNB_2001__13_1_137_0}
}
Gaál, István; Nyul, Gábor. Computing all monogeneous mixed dihedral quartic extensions of a quadratic field. Journal de théorie des nombres de Bordeaux, Volume 13 (2001) no. 1, pp. 137-142. http://www.numdam.org/item/JTNB_2001__13_1_137_0/

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