Constructing complete tables of quartic fields using Kummer theory

Cohen, Henri; Diaz y Diaz, Francisco; Olivier, Michel

doi:10.1090/S0025-5718-02-01452-7

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.

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