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We describe a new type of polycyclic presentations, that we will call refinedsolvable presentations, for polycyclic groups. These presentations are obtainedby refining a series of normal subgroups with abelian sections. Thesepresentations can be described effectively by presentation maps which yield thebasis data structure to define a polycyclic group in computer-algebra-systemslike {\scshape Gap} or {\scshape Magma}. We study refined solvablepresentations and, in particular, we obtain consistency criteria for them. Thisconsistency implementation demonstrates that it is often faster than theexisting methods for polycyclic groups.

Refined solvable presentations for polycyclic groups