Finding normal integral bases of cyclic number fields of prime degree
Let \(L\) be a cyclic number field of prime degree \(p\). The authors give an efficient algorithm to calculate normal integral bases in \(L\). The method avoids computations in large extension fields of \(L\). The problem is reduced to finding the generator of a principal ideal in the \(p\)-th cyclotomic field. The procedure is implemented in the algebraic number theory package KASH developed in Berlin. To illustrate the algorithm the authors computed normal bases in the first 1000 fields of E. Lehmer's parametric family of cyclic quintic fields.
scientific article; zbMATH DE number 1513053