>>> For example, suppose we are given labels {1,2} and {3,4},
>> Do you want to say {1,2} is *one* label?
> No, {1,2} should become the labels of the first isomorphism type
> and {3,4} the labels of the second.
After that I could approximate what you were trying to convey by your
first mail.
On 06/08/2007 08:59 PM, Martin Rubey wrote:
> Dear Ralf,
>
> I continued to work on the multisort species, but now I have the following
> design problem:
>
> a crucial step in producing the isomorphism types for the composition FoG is
> to
> produce a multiset of isomorphismtypes of G, each structure having the same
> cardinality. For example, suppose we are given labels {1,2} and {3,4}, and G
> is the species of graphs. We have two isomorphismtypes, namely the graph with
> one edge and the graph without edges. We now want to obtain three different
> sets, each containing two structures: (omitting many braces)
>
> 1 3 1 3 1 3
> | | , | ,
> 2 4 2 4 2 4
>
>
> Allowing repeated labels this is straightforward: I produce the
> isomorphismtypes of G[1,1], and then produce a multiset-composition of the
> result. If all labels have to be distinct, I would have to relabel the
> structures, i.e., I would do it as follows:
> 1 1
> isomorphismTypes([1,2])$G returns | and
> 2 2
>
> multiset composition thereof returns
>
> 1 1 1 1 1 1
> | | , | ,
> 2 2 2 2 2 2
>
> relabel the structures to obtain
>
> 1 3 1 3 1 3
> | | , | ,
> 2 4 2 4 2 4
>
>
> Do we really want to do this?
I don't want this. I don't think it is good or even necessary to return
something like
> multiset composition thereof returns
>
> 1 1 1 1 1 1
> | | , | ,
> 2 2 2 2 2 2
MultisetComposition should return a *representative* of an isomorphism
type and therefore all labels would be different right away. There
should be no need to do relabelling (which would be impossible anyway
since you cannot distinguish the first 1 from the second 1).
Ralf
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