Refined solvable presentations for polycyclic groups

We describe a new type of presentation that, when consistent, describes a polycyclic group. This presentation is obtained by re ning a series of normal subgroups with abelian sections. These presentations can be described e ectively in computeralgebra- systems like Gap or Magma. We study these presentations and, in particular, we obtain consistency criteria for them. The consistency implementation demonstrates that there are situations where the new method is faster than the existing methods for polycyclic groups.