Among the d.g. nearrings, the nearrings , , and are implemented. Some of the algorithms can use the d.g. property in order to run much more efficiently (e.g., membership tests, direct decompositions). In particular, the cardinalities of for all groups up to order 31 (previously considered to be a hard problem) have been computed and published in . These d.g. nearrings now form an important integral part of the nearrings library. The group-theoretic algorithms built in into GAP have proven particularly useful for this kind of nearrings.