Appendix A Generalised Distributive Property

The Distributive Law is an extremely useful tool for analysis and computation in mathematics and computer science. It can also be used to make algorithms more memory-efficient. For example, if we wish to take the DFT of a shifted signal, we can avoid storing the signal itself. While the Distributive Law is defined for the group of real numbers under additivity (R, +), we can also define a more general distributive property for the Abelian group defined by an aggregator ( R, null) . Note that while our solution holds for any function f, it focuses on the special cases α = 0,β = 0 and α = 1,β = 0 .