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I have list of the form

{y[-1], y[0], w'[1], y'[0], w'''[-1], z''[-1]}

and I would like to gather the elements together based on their heads to have

{{y[-1], y[0], y'[0]}, {w'[1], w'''[-1]}, {z''[-1]}}

My attempt so far has been to use

GatherBy[{y[-1], y[0], w'[1], y'[0], w'''[-1], z''[-1]}, FreeQ[Head[#], y] &]

which yields

{{y[-1], y[0], y'[0]}, {w'[1], w'''[-1], z''[-1]}}

I feel likes it's almost there and all it needs is to apply a similar function again on the subparts of the list above looking instead for heads that contain w and then z. But isn't there a more direct way to do what I want as this might become very cumbersome and slow when there are more than just three variables to check for ?

Thanks in advance.

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6
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Always start by looking at the FullForm:

{y[-1], y[0], w'[1], y'[0], w'''[-1], z''[-1]} // FullForm
List[
 y[-1],
 y[0],
 Derivative[1][w][1],
 Derivative[1][y][0],
 Derivative[3][w][-1], 
 Derivative[2][z][-1]
]
myHead[Derivative[_][h_][_]] := h
myHead[h_[___]] := h

GatherBy[{y[-1], y[0], w'[1], y'[0], w'''[-1], z''[-1]}, myHead]

enter image description here

You can of course add other definitions to myHead to declare certain parts of other expressions as the "head" for the purpose of this gathering.

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  • $\begingroup$ That's wizardry. Thanks very much $\endgroup$ – jrekier Feb 11 '17 at 22:58
  • $\begingroup$ @jrekier thanks :D $\endgroup$ – Mr.Wizard Feb 11 '17 at 23:02

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