A targeted Martinet search
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.
 Publication:

Mathematics of Computation
 Pub Date:
 June 2009
 DOI:
 10.1090/S0025571808021789
 Bibcode:
 2009MaCom..78.1109D