Soit un corps quadratique réel. Nous donnons un algorithme rapide pour déterminer tous les corps quartiques diédraux avec signature mixte, monogènes (i.e. ayant des bases d’entiers ) et contenant comme sous-corps. Nous déterminons également tous les générateurs des bases dans 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
Let be a given real quadratic field. We give a fast algorithm for determining all dihedral quartic fields with mixed signature having power integral bases and containing as a subfield. We also determine all generators of power integral bases in . 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
@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}, pages = {137--142}, publisher = {Universit\'e Bordeaux I}, volume = {13}, number = {1}, year = {2001}, zbl = {1065.11086}, mrnumber = {1838076}, language = {en}, url = {http://www.numdam.org/item/JTNB_2001__13_1_137_0/} }
TY - JOUR AU - Gaál, István AU - Nyul, Gábor TI - Computing all monogeneous mixed dihedral quartic extensions of a quadratic field JO - Journal de Théorie des Nombres de Bordeaux PY - 2001 DA - 2001/// SP - 137 EP - 142 VL - 13 IS - 1 PB - Université Bordeaux I UR - http://www.numdam.org/item/JTNB_2001__13_1_137_0/ UR - https://zbmath.org/?q=an%3A1065.11086 UR - https://www.ams.org/mathscinet-getitem?mr=1838076 LA - en ID - JTNB_2001__13_1_137_0 ER -
Gaál, István; Nyul, Gábor. Computing all monogeneous mixed dihedral quartic extensions of a quadratic field. Journal de Théorie des Nombres de Bordeaux, Tome 13 (2001) no. 1, pp. 137-142. http://www.numdam.org/item/JTNB_2001__13_1_137_0/
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