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# 4.2 Blackbox functions

Here are a few functions used in chapter RDS:A quick start. These are meant as black boxes for quick tests. Some of them make choices for you which might not be suitable to the chase you consider, so for serious studies, consider using the more complicated-looking functions above (an example for this comprises chapter RDS:An Example Program).

- `SignatureData(` Gdata`,` forbiddenSet`,` k`,` lambda`,` maxtest`) O`

  Let Gdata be a record as returned by `PermutationRepForDiffsetCalculations`. Let forbiddenSet the forbidden set (as set or group).

  k is the length of the relative difference set to be constructed and lambda the usual parameter. maxtest is the Then `SignatureData` calls `SignatureDataForNormalSubgroups` for normal subgroups of order at least `RootInt(Gdata.G)`. Here maxtest is an integer which determines how many permutations of a possible signature are checked to be a sorted signature. Choose a value of at least 105. Larger numbers here normaly result in better results when generating difference sets (making reduction more effective).

- `NormalSgsHavingAtMostNSigs(` sigdata`,` n`,` lengthlist`) F`

  Let sigdata be a list as returned by 'SignatureDataForNormalSubgroups', an integer n and a list of integers lengthlist. `NormalSgsHavingAtMostKSigs` filters sigdata and returns a list of records with components .subgroup and .sigs is returned, such that for every entry .subgroup is a normal subgroup of index in lengthlist having at most n signatures.

- `SuitableAutomorphismsForReduction(` Gdata`,` normalsg`) F`

  Given a normal subgroup normalsg of Gdata.G, the function returns a list containing the group of automorphisms of Gdata.G which stabilizes all cosets modulo normalsg. This group is returned as a group of permutations on Gdata.Glist (which is actually the right regular representation). The returned list can be used with `StartsetsInCoset`.

- `StartsetsInCoset(` ssets`,` coset`,` forbiddenSet`,` aim`,` autlist`,` sigdat`,` data`,` lambda`) F`

  Assume, we want to generate difference sets ``coset by coset'' modulo some normal subgroup. Let ssets be a (possibly empty) set of startsets, coset the coset from which to take the elements to append to the startsets from ssets. Furthermore, let aim be the size of the generated partial difference sets (that is, the size of the elements from ssets plus the number of elements to be added from coset). Let autlist be a list of groups of automorphisms (in permutation representation) to use with the reduction algorithm. Here the output from `SuitableAutomorphismsForReduction` can be used. And data and sigdat are the records as returned by `PermutationRepForDiffsetCalculations` and `SignatureDataForNormalSubgroups` (or `SignatureData`, alternatively). The parameter lambda is the usual one for difference sets (the number of ways of expressing elements outside the forbidden set as quotients).

  Then `StartsetsInCoset` returns a list of partial difference sets (a list of lists of integers) of length aim.

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