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Mathematics of Computation

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Non-primitive number fields of degree eight
and of signature $(2,3)$, $(4,2)$ and $(6,1)$
with small discriminant

Author: Schehrazad Selmane
Journal: Math. Comp. 68 (1999), 333-344
MSC (1991): Primary 11R11, 11R16, 11R29, 11Y40
MathSciNet review: 1489974
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Abstract: We give the lists of all non-primitive number fields of degree eight having two, four and six real places of discriminant less than 6688609, 24363884 and 92810082, respectively, in absolute value. For each field in the lists, we give its discriminant, the discriminant of its subfields, a relative polynomial generating the field over one of its subfields and its discriminant, the corresponding polynomial over $\mathbf Q$, and the Galois group of its Galois closure.

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Additional Information

Schehrazad Selmane
Affiliation: Université des Sciences et de la Technologie Houari Boumediene, Institut de Mathematiques, B.P. 32, El-Alia, Bab-Ezzouar 16111, Algiers, Algeria

Keywords: Quadratic fields, quartic fields, relative extensions, discriminant.
Received by editor(s): March 1, 1995
Received by editor(s) in revised form: September 11, 1996
Article copyright: © Copyright 1999 American Mathematical Society