Solving discriminant form equations via unit equations (Q2563698)

By a theoretical result of Györy, the task of solving discriminant form equations is reduced to the resolution of unit equations in the normal closure of the number field \(K\) under consideration. The author combines refinements of earlier methods of himself with the action of the Galois group on the unit group to reduce the number of exponential variables in those unit equations. This enables him to solve discriminant form equations in number fields of higher degree in case the relative degree \([\Gamma:K]\) of the normal closure \(\Gamma\) of \(K\) is small. The method is illustrated by an example with \([K:\mathbb{Q}]=6\) and \([\Gamma:K]=3\).