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Constructing complete tables of quartic fields using Kummer theory
Authors:
Henri Cohen, Francisco Diaz y Diaz and Michel Olivier
Journal:
Math. Comp. 72 (2003), 941-951
MSC (2000):
Primary 11Y40, 11R16, 11R29
Posted:
June 13, 2002
MathSciNet review:
1954977
Full-text PDF Free Access
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Abstract: We explain how to construct tables of quartic fields of discriminant less than or equal to a given bound in an efficient manner using Kummer theory, instead of the traditional (and much less efficient) method using the geometry of numbers. As an application, we describe the computation of quartic fields of discriminant up to  , the corresponding table being available by anonymous ftp.
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- K. Belabas, A fast algorithm to compute cubic fields, Math. Comp. 66 (1997), 1213-1237. MR 97m:11159
- 2.
- A.-M. Bergé, J. Martinet, and M. Olivier, The computation of sextic fields with a quadratic subfield, Math. Comp. 54 (1990), 869-884. MR 90k:11169
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- M. Bhargava, Gauss Composition and Generalizations, Proceedings ANTS V, Sydney (2002), Lecture Notes in Comp. Sci., Springer-Verlag (2002), to appear.
- 4.
- J. Buchmann and D. Ford, On the computation of totally real quartic fields of small discriminant, Math. Comp. 52 (1989), 161-174. MR 89f:11147
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- 9.
- -, Construction of tables of quartic fields, Proceedings ANTS IV, Leiden (2000), Lecture Notes in Comp. Sci. 1838, Springer-Verlag (2000), 257-268.
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- -, Tables of octic fields with a quartic subfield, Math. Comp. 68 (1999), 1701-1716. MR 99m:11132
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Additional Information
Henri Cohen
Affiliation:
Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
Email:
cohen@math.u-bordeaux.fr
Francisco Diaz y Diaz
Affiliation:
Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
Email:
diaz@math.u-bordeaux.fr
Michel Olivier
Affiliation:
Laboratoire A2X, U.M.R. 5465 du C.N.R.S., Université Bordeaux I, 351 Cours de la Libération, 33405 Talence Cedex, France
Email:
olivier@math.u-bordeaux.fr
DOI:
http://dx.doi.org/10.1090/S0025-5718-02-01452-7
PII:
S 0025-5718(02)01452-7
Received by editor(s):
October 18, 2000
Received by editor(s) in revised form:
September 26, 2001
Posted:
June 13, 2002
Article copyright:
© Copyright 2002 American Mathematical Society
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