Difference sets are represented by lists of integers. Every difference set is assumed to contain 1. This is assumed implicitly. So the lists representing difference sets must not contain 1 (a partial difference set of length n is hence represented by a list of length n−1). If a partial difference set contains 1, many functions will produce errors.
To find Difference sets in a group, say G, begin with generating the group (and forbidden subgroup) and defining the parameters. Like this:
gap> LoadPackage("rds"); ---------------------------------------------------------------- Loading RDS 0.9beta5 by Marc Roeder For help, type: ?RDS ---------------------------------------------------------------- true gap> k:=9;;lambda:=1;;groupOrder:=81;; gap> forbiddenGroupOrder:=9;; gap> G:=ElementaryAbelianGroup(groupOrder); <pc group of size 81 with 4 generators> gap> Gdata:=PermutationRepForDiffsetCalculations(G);; gap> N:=Group(GeneratorsOfGroup(G){[1,2]}); <pc group with 2 generators> gap> Size(N)=forbiddenGroupOrder; #just a test... true
Once we have calculated Gdata, this will be used very often to represent the group G as it contains much more information.
RDS manual