I agree that this is a decision that would have to weigh between cost in 
speed and convenience.  For small values of n the speedup will be small but 
that is where order is more useful.  For large values of n the order is 
probably less important.  Correct results are clearly the most important 
consideration.

-Mike

On Tuesday, 17 March 2015 07:51:53 UTC-4, Nathann Cohen wrote:
>
> Hello, 
>
> > I think that Partitions should be output in either lex (or possibly 
> reverse 
> > lex) since this order is compatible with dominance order. 
>
> I only want to bring to your attention that deciding in which order 
> the partitions should be returned is not free in terms of 
> computational time. 
>
> The current implementation returns them in lex order, but returns 
> *many* wrong answers too (see #17548). 
>
> In order to fix that, Jeroen is re-implementing this feature through a 
> routine that enumerates the integer points of a polytope (see #17920), 
> probably without any control over the order in which they are 
> returned. 
>
> Thus, in order for Partition/Composition to return them in a specific 
> order we must list them *all* before returning the first of them. This 
> can really mean hours (or no results at all) instead of seconds on big 
> instances. 
>
> Nathann 
>

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