Diaz y Diaz, Francisco; Olivier, M. Imprimitive ninth-degree number fields with small discriminants. (English) Zbl 0819.11070 Math. Comput. 64, No. 209, 305-321, microfiche suppl. (1995). Known methods for computing algebraic number fields of small degree and small (absolute) discriminants were applied successfully up to degree 8 (for totally real fields). Considering imprimitive fields is somewhat easier. Consequently the authors compute tables of ninth degree fields of small discriminant which contain cubic subfields. They employ a theorem of J. Martinet [Théorie des Nombres, Sémin. Delange-Pilot- Poitou, Paris 1983-84, Prog. Math. 59, 147-179 (1985; Zbl 0567.12009)] to derive bounds for the coefficients of a generating cubic polynomial over a cubic subfield. The calculated tables contain a great deal of interesting data on a total of 1112 ninth degree number fields. These data are included by microfiche. Reviewer: M.Pohst (Berlin) Cited in 6 Documents MSC: 11Y40 Algebraic number theory computations 11R21 Other number fields 11-04 Software, source code, etc. for problems pertaining to number theory 11R16 Cubic and quartic extensions Keywords:tables of ninth degree fields of small discriminant; cubic subfields; cubic polynomials Citations:Zbl 0567.12009 Software:KANT/KASH × Cite Format Result Cite Review PDF Full Text: DOI