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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