A table of quintic number fields

Schwarz, A.; Pohst, M.; Diaz y Diaz, F.

doi:10.1090/S0025-5718-1994-1219705-3

A table of quintic number fields
HTML articles powered by AMS MathViewer

by A. Schwarz, M. Pohst and F. Diaz y Diaz PDF

Math. Comp. 63 (1994), 361-376 Request permission

Abstract:

All algebraic number fields F of degree 5 and absolute discriminant less than $2 \times {10^7}$ (totally real fields), respectively $5 \times {10^6}$ (other signatures) are determined. We describe the methods which we applied and list significant data.

References

Erwin H. Bareiss, Sylvester’s identity and multistep integer-preserving Gaussian elimination, Math. Comp. 22 (1968), 565–578. MR 226829, DOI 10.1090/S0025-5718-1968-0226829-0
Johannes Buchmann and David Ford, On the computation of totally real quartic fields of small discriminant, Math. Comp. 52 (1989), no. 185, 161–174. MR 946599, DOI 10.1090/S0025-5718-1989-0946599-1
Johannes Buchmann, David Ford, and Michael Pohst, Enumeration of quartic fields of small discriminant, Math. Comp. 61 (1993), no. 204, 873–879. MR 1176706, DOI 10.1090/S0025-5718-1993-1176706-0
F. Diaz y Diaz, A table of totally real quintic number fields, Math. Comp. 56 (1991), no. 194, 801–808, S1–S12. MR 1068820, DOI 10.1090/S0025-5718-1991-1068820-3
D. Ford, Enumeration of totally complex quartic fields of small discriminant, Computational number theory (Debrecen, 1989) de Gruyter, Berlin, 1991, pp. 129–138. MR 1151860
John Hunter, The minimum discriminants of quintic fields, Proc. Glasgow Math. Assoc. 3 (1957), 57–67. MR 91309
Nikola Obreschkoff, Verteilung und Berechnung der Nullstellen reeller Polynome, VEB Deutscher Verlag der Wissenschaften, Berlin, 1963 (German). MR 0164003
Michael Pohst, Berechnung kleiner Diskriminanten total reeller algebraischer Zahlkörper, J. Reine Angew. Math. 278(279) (1975), 278–300 (German). MR 387242, DOI 10.1515/crll.1975.278-279.278
Michael Pohst, On the computation of number fields of small discriminants including the minimum discriminants of sixth degree fields, J. Number Theory 14 (1982), no. 1, 99–117. MR 644904, DOI 10.1016/0022-314X(82)90061-0
M. Pohst, On computing isomorphisms of equation orders, Math. Comp. 48 (1987), no. 177, 309–314. MR 866116, DOI 10.1090/S0025-5718-1987-0866116-2
M. Pohst, J. Martinet, and F. Diaz y Diaz, The minimum discriminant of totally real octic fields, J. Number Theory 36 (1990), no. 2, 145–159. MR 1072461, DOI 10.1016/0022-314X(90)90069-4
M. Pohst and H. Zassenhaus, Algorithmic algebraic number theory, Encyclopedia of Mathematics and its Applications, vol. 30, Cambridge University Press, Cambridge, 1989. MR 1033013, DOI 10.1017/CBO9780511661952

Berechnung von Zahlkörpen fünften Grades mit kleiner Diskriminante

J. Graf von Schmettow, KANT—a tool for computations in algebraic number fields, Computational number theory (Debrecen, 1989) de Gruyter, Berlin, 1991, pp. 321–330. MR 1151875
Carl Ludwig Siegel, The trace of totally positive and real algebraic integers, Ann. of Math. (2) 46 (1945), 302–312. MR 12092, DOI 10.2307/1969025
Richard P. Stauduhar, The determination of Galois groups, Math. Comp. 27 (1973), 981–996. MR 327712, DOI 10.1090/S0025-5718-1973-0327712-4

Algebra

Hans Zassenhaus, On the second round of the maximal order program, Applications of number theory to numerical analysis (Proc. Sympos., Univ. Montréal, Montreal, Que., 1971) Academic Press, New York, 1972, pp. 389–431. MR 0371862