On 01/04/2007 12:13 PM, Martin Rubey wrote:
> Dear all,
> 
> I'm sick, so just a short update and reply.

Please don't answer my mails. Go to bed and recover. Get well soon.

>> But still, the problem is finite and thus solvable in principle by applying
>> all permutations from S_n and building cosets.
> 
> I don't think this is entirely true. What we need for a "stupid" algorithm to
> do the unlabelled case - not the cases "inbetween" - is a function in, say,
> CartesianProduct
> 
> coerce: % -> IsomorphismType
> 
> that yields the isomorphism Type of a structure. Please show me how to do that
> for the Cartesian Product! (This would be the equivalent to having a normal
> form)

If I define IsomorphismType to be Set(%) then the only thing I have to 
do in the coerce function to generate all orbit elements with respect to 
S_n. The orbit is a normal form if you like. An ugly one, I agree, but 
otherwise I see nothing wrong with it.

> An alternative possibility is to generate the structures, and for each
> generated structure check whether it is isomorphic to one of the structures
> already generated.

That's probably the same thing.

Ralf

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