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# 4 Invariants for Difference Sets

### Sections

1. The Coset Signature
2. Blackbox functions

This chapter contains an important tool for the generation of difference sets. It is called the ``coset signature'' and is an invariant for equivalence of partial relative difference sets. For large λ, there is an invariant calculated by `MultiplicityInvariantLargeLambda`. This invariant can be used complementary to the coset signature and is explained in section Ordered signatures by quotient images.

Most of the methods explained here are not commonly used. If you do not want to know how coset signatures work in detail, you can safely skip a large part of this and go straight to the explanation of `SignatureDataForNormalSubgroups` and `ReducedStartsets`.

The last section (RDS:Blackbox functions) of this chapter has some functions which allow the user to use coset signatures with even less effort. But be aware that these functions make choices for you that you probably do not want if you do very involved calculations. In particular, the coset signatures are not stored globally and hence cannot be reused. For a demonstration of these easy-to-use functions, see chapter RDS:A quick start

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