On the computation of unit groups and class groups of totally real quartic fields
HTML articles powered by AMS MathViewer
- by J. Buchmann, M. Pohst and J. von Schmettow PDF
- Math. Comp. 53 (1989), 387-397 Request permission
Abstract:
In this paper we describe the computation of a system of fundamental units and of the class group for each totally real quartic field $\mathcal {F}$ of discriminant less than ${10^6}$. Generating equations, integral bases, and the Galois groups for all those fields were recently given by Buchmann and Ford.References
- Johannes Buchmann, On the computation of units and class numbers by a generalization of Lagrange’s algorithm, J. Number Theory 26 (1987), no. 1, 8–30. MR 883530, DOI 10.1016/0022-314X(87)90092-8
- Johannes Buchmann, On the period length of the generalized Lagrange algorithm, J. Number Theory 26 (1987), no. 1, 31–37. MR 883531, DOI 10.1016/0022-314X(87)90093-X
- 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
- H. Cohen and J. Martinet, Class groups of number fields: numerical heuristics, Math. Comp. 48 (1987), no. 177, 123–137. MR 866103, DOI 10.1090/S0025-5718-1987-0866103-4
- P. D. Domich, R. Kannan, and L. E. Trotter Jr., Hermite normal form computation using modulo determinant arithmetic, Math. Oper. Res. 12 (1987), no. 1, 50–59. MR 882842, DOI 10.1287/moor.12.1.50
- U. Fincke and M. Pohst, Improved methods for calculating vectors of short length in a lattice, including a complexity analysis, Math. Comp. 44 (1985), no. 170, 463–471. MR 777278, DOI 10.1090/S0025-5718-1985-0777278-8
- Donald E. Knuth, The art of computer programming. Vol. 2, 2nd ed., Addison-Wesley Series in Computer Science and Information Processing, Addison-Wesley Publishing Co., Reading, Mass., 1981. Seminumerical algorithms. MR 633878
- P. Noordzij, Über das Produkt von vier reellen, homogenen, linearen Formen, Monatsh. Math. 71 (1967), 436–445 (German). MR 230686, DOI 10.1007/BF01295135
- Michael Pohst and Hans Zassenhaus, Über die Berechnung von Klassenzahlen und Klassengruppen algebraischer Zahlkörper, J. Reine Angew. Math. 361 (1985), 50–72 (German). MR 807252, DOI 10.1515/crll.1985.361.50
- 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
- Robert Remak, Über Grössenbeziehungen zwischen Diskriminante und Regulator eines algebraischen Zahlkörpers, Compositio Math. 10 (1952), 245–285 (German). MR 54641 J. Graf V. Schmettow, Über die Berechnung von Klassengruppen algebraischer Zahlkörper, Diplomarbeit, Düsseldorf, 1987.
Additional Information
- © Copyright 1989 American Mathematical Society
- Journal: Math. Comp. 53 (1989), 387-397
- MSC: Primary 11Y40; Secondary 11R16, 11R27, 11R80
- DOI: https://doi.org/10.1090/S0025-5718-1989-0970698-1
- MathSciNet review: 970698