>> If I am not completely wrong, the cycle index composition should work,
>
> WOW!
testBell() in test/species.as.nw works and it checks against explicit
values. That tests cycleIndexSeries $ SetPartition.
Furthermore the following test also succeeds
<<test polynomial series>>=
testPartitionViaCompose(): () == {
macro {
V == CycleIndexVariable;
T == SparseIndexedPowerProduct(V, I);
P == SparseDistributedPolynomial(Q, V, T);
S == CycleIndexSeries;
}
import from P, DataStream P;
cisPartition: S := cycleIndexSeries $ SetPartition(Z);
cisSet: S := cycleIndexSeries $ SetSpecies(Z);
local g: Generator P := generate {
yield 0$P; -- constant term
for n:I in 1.. repeat yield coefficient(cisSet, n);
}
cisNonEmptySet: S := stream(g)::S;
cisPart: S := compose(cisSet, cisNonEmptySet);
checkEquals(cisPartition, cisPart);
}
@
which is at least something, because the computation of cisPartition
does not involve "compose", but rather uses the explicit formula given
in BLL.
Still, there lurks a bug somewhere...
Ralf
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