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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

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A table of totally real cubic fields
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by I. O. Angell PDF
Math. Comp. 30 (1976), 184-187 Request permission

Abstract:

In this paper the author describes the construction of a table of totally real cubic number fields. Each field is distinguished by the coefficients of a generating polynomial, the index of this polynomial over the field and the discriminant of the field. The class number and a fundamental pair of units is also given.
References
  • I. O. Angell, A table of complex cubic fields, Bull. London Math. Soc. 5 (1973), 37–38. MR 318099, DOI 10.1112/blms/5.1.37
  • P. BACHMANN, Allgemeine Arithmetik der Zahlkörper, Leipzig, 1905. H. DAVENPORT, "On the product of three homogeneous linear forms. II," Proc. London Math. Soc. (2), v. 44, 1938; pp. 412-431.
  • H. Davenport and H. Heilbronn, On the density of discriminants of cubic fields, Bull. London Math. Soc. 1 (1969), 345–348. MR 254010, DOI 10.1112/blms/1.3.345
  • B. N. Delone and D. K. Faddeev, Theory of Irrationalities of Third Degree, Acad. Sci. URSS. Trav. Inst. Math. Stekloff, 11 (1940), 340 (Russian). MR 0004269
  • H. J. Godwin, On totally complex quartic fields with small discriminants, Proc. Cambridge Philos. Soc. 53 (1957), 1–4. MR 82527
  • H. J. Godwin and P. A. Samet, A table of real cubic fields, J. London Math. Soc. 34 (1959), 108–110. MR 100579, DOI 10.1112/jlms/s1-34.1.108
  • D. SHANKS, "Review of I. O. Angell, A table of complex cubic fields," Math. Comp.,v. 29, 1975, pp. 661-665. RMT 33.
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Additional Information
  • © Copyright 1976 American Mathematical Society
  • Journal: Math. Comp. 30 (1976), 184-187
  • MSC: Primary 12A30
  • DOI: https://doi.org/10.1090/S0025-5718-1976-0401701-6
  • MathSciNet review: 0401701