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# 2.1 First Step: Integers instead of group elements

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.

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