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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Tenth degree number fields with quintic fields having one real place
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by Schehrazad Selmane PDF
Math. Comp. 70 (2001), 845-851 Request permission


In this paper, we enumerate all number fields of degree $10$ of discriminant smaller than $10^{11}$ in absolute value containing a quintic field having one real place. For each one of the $21509$ (resp. $18167)$ found fields of signature $(0,5)$ (resp. $(2,4))$ the field discriminant, the quintic field discriminant, a polynomial defining the relative quadratic extension, the corresponding relative discriminant, the corresponding polynomial over $\mathbb {Q}$, and the Galois group of the Galois closure are given. In a supplementary section, we give the first coincidence of discriminant of $19$ (resp. $20)$ nonisomorphic fields of signature $(0,5)$ (resp. $(2,4))$.
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Additional Information
  • Schehrazad Selmane
  • Affiliation: University of Sciences and Technology (U.S.T.H.B), Institut of Mathematics, B.P. 32 El Alia, Bab-Ezzouar, 16111, Algiers, Algeria
  • Email:
  • Received by editor(s): November 3, 1998
  • Received by editor(s) in revised form: April 27, 1999
  • Published electronically: July 13, 2000
  • © Copyright 2000 American Mathematical Society
  • Journal: Math. Comp. 70 (2001), 845-851
  • MSC (2000): Primary 11R11, 11R29, 11Y40
  • DOI:
  • MathSciNet review: 1709158