parallelization - Operators without built-in meaning are incompatible with parallel evaluation

Mathematica has a useful set of Operators Without Built-In Meanings. For example: CenterDot, CircleDot, CirclePlus, Star, etc. According to the linked documentation, a user is allowed to define evaluation rules for these symbols. Unfortunately, these symbols are not compatible with parallel evaluation. The following example shows how parallel evaluation leads to an incorrect result when user-defined evaluation rule for CenterDot is used:

CenterDot = Times;
DistributeDefinitions[CenterDot];
f[n_] := Coefficient[CenterDot[n, x], x];


Table[f[n],{n,1,5}]

{1,2,3,4,5} (* correct *)

ParallelTable[f[n],{n,1,5}]

{0,0,0,0,0} (* wrong *)

I think that the root cause of this bug is that parallel evaluation routines are not allowed to distribute definitions of any symbols from System context while all Operators Without Built-In Meanings are defined in this very context.

Is there a practical way to use Operators Without Built-In Meanings in parallel calculations?

This question is based on observations made here, where accepted workaround was just to abandon such operators altogether.

Comments

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I need to fit an implicitly defined curve. I thought I could get some data out of Solve , and then using FindFit . Therefore, I would like to find the relation the parametric curve defined by $F(x,y)=0$: Solve[-(1/2) + 1/2 (0.41202 BesselK[0, 0.1 Sqrt[x^2 + y^2]] + (0.101483 x BesselK[1, 0.1 Sqrt[x^2 + y^2]])/Sqrt[x^2 + y^2]) == 0, y] But I can't get an output: Solve was unable to solve the system with inexact coefficients or the system obtained by direct rationalization of inexact numbers present in the system. Since many of the methods used by Solve require exact input, providing Solve with an exact version of the system may help. >> Edit: In particular, I would like to fit the data coming from the curve with the expression of another curve, and not with a function $f(x)$. In particular, since this clearly looks like a cardioid , I would like it to fit to something like it. What other strategies could I try?

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