A targeted Martinet search

Driver, Eric; Jones, John

doi:10.1090/S0025-5718-08-02178-9

A targeted Martinet search
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by Eric D. Driver and John W. Jones PDF

Math. Comp. 78 (2009), 1109-1117 Request permission

Abstract:

Constructing number fields with prescribed ramification is an important problem in computational number theory. In this paper, we consider the problem of computing all imprimitive number fields of a given degree which are unramified outside of a given finite set of primes $S$ by combining the techniques of targeted Hunter searches with Martinet’s relative version of Hunter’s theorem. We then carry out this algorithm to generate complete tables of imprimitive number fields for degrees $4$ through $10$ and certain sets $S$ of small primes.

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