On the computation of totally real quartic fields of small discriminant
Johannes A Buchmann, David James Ford · Mathematics of Computation · 1989
All totally real quartic fields of discriminant less than 10 6 {10^6} are computed. The method used to generate the fields is derived from Delone and Faddeev, with corrections and improvements. A new method for deciding field isomorphism is used to eliminate redundant examples. Integral bases and Galois groups are given for each field.