Just one data point that may be relevant -- blame shows the comment as 
dating from 2012.

The code for multiset partitions has changed since then.

Before pull request 1658, by Chris Smith, multiset_partitions gave bad 
results.   1658 is from about the same time as the comment.

Later, (pr 1848) I replaced Chris' implementation with a faster algorithm. 
The current ordering is deterministic, but I would be surprised if it were 
the same as the old algorithm. 

I don't claim any knowledge of Meijer integration, but I don't remember 
breaking any tests there.

On Monday, March 23, 2015 at 11:21:04 AM UTC-7, Joachim Durchholz wrote:
>
> Hi all, 
>
> this probably mostly goes to Tom Bachmann and Chris Smith, but maybe 
> others know a bit about Meijer integration. 
>
> I'm working on something that changes the internal ordering of terms a 
> bit, and Meijer seems to rely on the current ordering for some 
> vaguely-explained benefits; I need to find out whether it's relevant or 
> not. 
>
> Specifically, during 
> sympy/integrals/tests/test_integrals.py:test_issue_8368 , 
> I see a call to _rewrite2(f, x) with 
>    f = Mul: exp(_x)*exp(-_x*s)/2 and 
>    x = Dummy: _x 
> (it seems only f is relevant here). 
>
> The docstring for _rewrite2 talks about multiset_partitions returning 
> stuff in a canonical (but not always optimal) order. Frustratingly, it 
> does not really explain what the problem is, nor what will fail if the 
> order is changed. 
>
> It might be ultimately irrelevant though, as further processing filters 
> the result through ordered() in _rewrite2. If that's the case, then 
> maybe the docstring of _rewrite2 is wrong about test cases breaking, so 
> I'm unsure whether my current understanding of what's going on is 
> missing something important. 
>
> Any tips, pointers and explanations appreciated. 
>
> Regards, 
> Jo 
>

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