(I hope you don't mind that I forward to aldor-combinat.  But I'll describe an
idea below, that I want to archive there...)

"Mike Hansen" <[EMAIL PROTECTED]> writes:

> > This looks deceptively simple.  Are you sure it's correct?
> 
> This is just for ordinary species.  

what is an "ordinary species"?  You mean, it's only for the structures, not the
isotypes?

> The only differences between it and your code for isomorphism types is that I
> use the getattr stuff to avoid writing the same algorithm twice and that I
> use CartesianProduct which I had already written elsewhere in Sage.

Are you saying that you took the algorithm from trunk?  If so, then it's
incorrect.  Unfortunately, I don't have an example right now, but I think there
should be an appropriate test in our testsuite (which is failing in trunk, of
course).  I should make it explicit, I admit.

I'd be *very* interested in a *good* design for isotypes that works with
representatives.  I think one way to do it would be to separate the structure
from it's labels.  More precisely, a structure could be represented as an
"isotype" together with a bijection that gives the structure the appropriate
labelling.  Of course, this representation is not unique, i.e. we can
represent, say, the binary tree

(1,(2,3))

as 

isotype = (1,(2,3)) - pi = id

or as

isotype = (2,(1,3)) - pi = 2->1, 1->2, 3->3

But maybe, this wouldn't matter for the generation of compositions as long as
the representation is deterministic.

Martin


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