[sage-combinat-devel] Re: [sage-devel] Categories for the working programmer

[Ralf Hemmecke]

You know that FriCAS/Aldor does not have this drawback? Eg., the set of all
combinatorial species forms a Ring...

A semi-ring, we don't have virtual species yet.

Thanks for pointing this out. Could you make a quick summary here of
how this is achieved?

I don't know what Martin refers to exactly, because he could have
pointed to some code.

Each combinatorial species is a domain, right? Are they simultaneously
elements of some domain in the Ring category?

Well, that is not completely fleshed out. (At least not in trunk of
aldor-combinat.) But as you see at

http://www.risc.uni-linz.ac.at/people/hemmecke/AldorCombinat/combinatsu27.html#x41-590008.14

you are approximately right.

Elements of this CombinatorialSpeciesAlgebra domain are functions that
produce combinatorial species. The 1 is clear, addition as well, 0 would
also be simple. The X, maybe doesn't really belong there, since that
already is a step towards a polynomial (semi)algebra. But otherwise, who
cares at the moment?

Well, that is just some idea... And I don't see why that cannot work in
Aldor. I actually also don't see a big trouble that something along
these lines would be impossible in Python. Or is it? I'd be happy to
learn more how this can be achieved through python.

Ralf

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