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A table of quintic number fields
Authors:
A. Schwarz, M. Pohst and F. Diaz y Diaz
Journal:
Math. Comp. 63 (1994), 361-376
MSC:
Primary 11Y40; Secondary 11R21, 11R32
MathSciNet review:
1219705
Full-text PDF Free Access
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Additional Information
Abstract: All algebraic number fields F of degree 5 and absolute discriminant less than (totally real fields), respectively (other signatures) are determined. We describe the methods which we applied and list significant data.
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- [1]
- E. H. Bareiss, Sylvester's identity and multistep integer preserving Gaussian elimination, Math. Comp. 22 (1968), 565-578. MR 0226829 (37:2416)
- [2]
- J. Buchmann and D. J. Ford, On the computation of totally real quartic fields of small discriminant, Math. Comp. 52 (1989), 161-174. MR 946599 (89f:11147)
- [3]
- J. Buchmann, D. Ford, and M. Pohst, Enumeration of quartic fields of small discriminant, Math. Comp. 61 (1993), 873-879. MR 1176706 (94a:11164)
- [4]
- F. Diaz y Diaz, A table of totally real quintic number fields, Math. Comp. 56 (1991), 801-808. MR 1068820 (91h:11155)
- [5]
- D. Ford, Enumeration of totally complex quartic fields of small discriminant, Computational Number Theory, Proc. Colloq. on Comp. Number Theory (Debrecen, Hungary, 1989) (A. Pethö, M. E. Pohst, H. C. Williams, and H. G. Zimmer, eds.), de Gruyter, Berlin and New York, 1991, pp. 129-138. MR 1151860 (93b:11140)
- [6]
- J. Hunter, The minimum discriminant of quintic fields, Proc. Glasgow Math. Assoc. 3 (1957), 57-67. MR 0091309 (19:944b)
- [7]
- N. Obreschkoff, Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963. MR 0164003 (29:1302)
- [8]
- M. Pohst, Berechnung kleiner Diskriminanten total reeller algebraischer Zahlkörper, J. Reine Angew. Math. 278/279 (1975), 278-300. MR 0387242 (52:8085)
- [9]
- -, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory 14 (1982), 99-117. MR 644904 (83g:12009)
- [10]
- -, On computing isomorphisms of equation orders, Math. Comp. 48 (1987), 309-314. MR 866116 (88b:11066)
- [11]
- M. Pohst, J. Martinet, and F. Diaz y Diaz, The minimum discriminant of totally real octic fields, J. Number Theory 36 (1991), 145-159. MR 1072461 (91g:11128)
- [12]
- M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Cambridge Univ. Press, Cambridge, 1989. MR 1033013 (92b:11074)
- [13]
- A. Schwarz, Berechnung von Zahlkörpen fünften Grades mit kleiner Diskriminante, Diplomarbeit, Heinrich-Heine-Universität Düsseldorf, 1991.
- [14]
- J. Graf von Schmettow, KANT-a tool for computations in algebraic number fields, Computational Number Theory (A. Pethö, M. E. Pohst, H. C. Williams, and H. G. Zimmer, eds.), de Gruyter, Berlin and New York, 1991, pp. 321-330. MR 1151875 (92m:11151)
- [15]
- C. L. Siegel, The trace of totally positive and real algebraic integers, Ann. of Math. (2) 46 (1945), 302-312. MR 0012092 (6:257a)
- [16]
- R. P. Stauduhar, The determination of Galois groups, Math. Comp. 27 (1973), 981-996. MR 0327712 (48:6054)
- [17]
- B. L. van der Waerden, Algebra. I, 8th ed., Heidelberger Taschenbücher 12, Springer-Verlag, Berlin, Heidelberg, New York, 1971.
- [18]
- H. Zassenhaus, On the second round of the maximal order program, Applications of Number Theory to Numerical Analysis, Academic Press, New York, 1972, pp. 398-431. MR 0371862 (51:8079)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0025-5718-1994-1219705-3
PII:
S 0025-5718(1994)1219705-3
Article copyright:
© Copyright 1994 American Mathematical Society
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