A targeted Martinet search
Eric D. Driver, John W. Jones · Mathematics of Computation · 2008
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 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 4 through 10 10 and certain sets S S of small primes.