[see also: talk]
Roughly speaking, we shall produce a synthesis of index theory with Fourier analysis.
Strictly speaking, we should write something like $a(l,m,n)$ to reflect the dependence; we shall rely upon context instead.
Hence, although the topology of reducts of $A$ is uniformly controlled, so to speak, by that of $A$, the model theory of the reducts can be much wilder.
The two polygons $P$ and $P'$ are the two ends of the orbit, so to speak.
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