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I have the following code where ParallelSubmit called on OverBar does not return the same result as non-parallel code even though I used DistributeDefinitions. Without the OverBar it works fine. The code

A = Sum[lambda[order] (r - rp)^order, {order, 0, 2}];
OverBar[x_ + y_] := OverBar[x] + OverBar[y];
OverBar[x_ y_] := OverBar[x] OverBar[y];
OverBar[x_ /; NumericQ[x]] := Conjugate[x]
OverBar[x_[xa__]] := OverBar[x][xa]
OverBar[x_ /; MemberQ[RealSymbols, x]] := x
DefaultRealSymbols = {Power, r, rp};
RealSymbols = DefaultRealSymbols;
DistributeDefinitions[A, OverBar];

Coefficient[A, r - rp, 2]
WaitAll[ParallelSubmit[Coefficient[A, r - rp, 2]]]
Coefficient[OverBar[A], r - rp, 2]
WaitAll[ParallelSubmit[Coefficient[OverBar[A], r - rp, 2]]]

returns

lambda[2]
lambda[2]
\!\(\*OverscriptBox[\(lambda\), \(_\)]\)[2]
0

where the 0 should be \!\(\*OverscriptBox[\(lambda\), \(_\)]\)[2].

What am I doing wrong?

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  • $\begingroup$ Have you checked that evaluating the command using ParallelEvaluate works as expected? $\endgroup$ – mmeent Jun 13 '18 at 18:09
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    $\begingroup$ You are doing nothing wrong. When I run your code with OverBar replaced with overbar, it works. The same applies when I use ParallelEvaluate instead of WaitAll. So it looks like a bug to me. At least, it is unexpected behaviour, as you said. $\endgroup$ – Fred Simons Jun 13 '18 at 18:55
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The problem seems to be that DistributeDefinitions does not work for any of the built-in operators without built-in meaning. You can check by running

ParallelEvaluate@DownValues@OverBar

that none of the custom DownValues have been distributed to the parallel kernels.

As a work around you could wrap your definitions for OverBar in a ParallelEvaluate to evaluate the definitions on the parallel kernels. Alternatively, you can put your definitions in a package, and load it using ParallelNeeds. This has the advantage that the definitions will reload on any newly (re)started kernel.

Finally, you could change you definitions to not use the built-in OverBar operator but say overbar. You can then get Mathematica to put the Over bar in the output using

Format[overbar[x_]] := OverBar[x]
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