## Constructing complete tables of quartic fields using Kummer theory

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- by Henri Cohen, Francisco Diaz y Diaz and Michel Olivier PDF
- Math. Comp.
**72**(2003), 941-951 Request permission

## 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 $10^7$, the corresponding table being available by anonymous ftp.## References

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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
- Received by editor(s): October 18, 2000
- Received by editor(s) in revised form: September 26, 2001
- Published electronically: June 13, 2002
- © Copyright 2002 American Mathematical Society
- Journal: Math. Comp.
**72**(2003), 941-951 - MSC (2000): Primary 11Y40, 11R16, 11R29
- DOI: https://doi.org/10.1090/S0025-5718-02-01452-7
- MathSciNet review: 1954977