Cannot retrieve a function definition from file after save with ParallelDo

Question

This is an example of a problem I have retrieving functions from a file I save using ParalleDo.

(*save data to a file in ParallelDo loop*)

myF[x_] := 2 + x^2 + 3 x^3;

fileName = StringTemplate["D:\\mathematica\\file`1`.m"];

ParallelDo[
  theDeriv = D[myF[x], x];
  Export[fileName[i], Definition@theDeriv],
  {i, 1, 5}
  ];

And if I retrieve the function while in this notebook using:

fileName = StringTemplate["D:\\mathematica\\file`1`.m"];
deriv = Import[fileName[1]]

It returns the derivative:

2 x + 9 x^2

However if I first close Mathematica then re-open this notebook and just retrieve the function by first executing Import, it returns what looks like unusable temporary variable names:

2 Notebook$$16$203416`x + 9 Notebook$$16$203416`x^2

If I just use Do this does not happen but I need to run much more complicated code saving many files and would like to do so in parallel. Can someone help me to get this to work in parallel?

Thank you.

Answer 1

Try the following. Notice definition for fileName as well as a slightly different function, so that different derivatives can be calculated (one for each file).

myF[x_] := 2 + x^2 + 3 x^3 + 4 x^4 + 5 x^5;
fileName[k_Integer] := 
 StringTemplate["L:\\mathematica\\file`1`.m"][ToString@k]

In a separate cell, do what you are doing: (I am calculating a few derivatives and four kernels are launched on my system to perform these calcs. Five files are created and if already there, these are overwritten. Choose filepath according to your system.)

ParallelDo[theDeriv = D[myF[x], {x, i}];
  Export[fileName[i], Definition@theDeriv], {i, 1, 5}];

After quitting the kernel (or restarting Mma), definitions such as fileName are not there.You can either load a file directly (It is read as an expression):

deriv = Import["L:\\mathematica\\file2.m"]

2 + 18 x + 48 x^2 + 100 x^3

or evaluate fileName again, after which:

deriv = Import[fileName[1]]

2 x + 9 x^2 + 16 x^3 + 25 x^4