>> Why can't we use
>>
>>    Subsets = SetSpecies * SetSpecies
> 
> because "Times" needs "Subsets".

Ah... OK this justifies Subset. (Same as Partition for Compose.)

> Does this contradict your design, that generating series do not need to
 > know about species?  (I didn't understand this
> design concept, so I might have the wording wrong)

The wording goes: Remove the concept of "species" and all domains and 
functions related to it from AC and the rest will still compile and it 
will contain *everything* that appears in src/series.as.nw and 
src/gseries.as.nw. The species concept builds on the concept of 
FormalPowerSeries and ...GeneratingSeries, but *not* vice versa.

I've just looked at your code... and I will immediately remove the 
function export

coerce: % -> Record(subset: SetSpecies L, rest: SetSpecies L);

because Records are a pain in further use. What you actually want is

coerce: % -> SetSpecies L;

subsetAndComplement: % -> Cross(SetSpecies L, SetSpecies L)

You could also leave out the "Cross".

If I now look at the last function... a "subset" always knows about its 
superset. Interesting.

I also don't know whether "subsetAndComplement" is the best name for the 
function.

>> PS2: Are you documenting your code?
> 
> I was going to document Subsets and Combinations today.  But if you think they
> are unnecessary, I won't.  I simply have too much work to do.

I am for Subsets, but don't bother with Combinatitions. We can implement 
this later if we really need efficiency.

> What I'll definitively do is look at the excercise for FunctorialComposition

I really wonder what that would help for my wish not to sum over 
permuations.

Ralf

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