I have a list of gradient components, $ partial f / partial x_i $, of a function $ f (x_1, x_2, cdots) $. Is there a good way to rebuild the function $ f $?
One approach to doing this would be to treat this as an EDP system and to use
DSolve. However, Mathematica is unable to resolve PDEs with more than 3 variables – see, for example, here.
Another approach is to integrate the gradients $ int ( partial f / partial x_i) dx_i $ then take the
Union terms of all integrals. This is not a robust enough way to do things because it fails if expressions for integrals are not simple enough (
ExpandAll do not help). A code for doing this is as follows: