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Differentiation inside package




I am trying to put all my functions in a single package and some of them do not work because of differentiation. Suppose I have the following package


BeginPackage["Diff`"] 
Diff[yy_]:=Module[{cc},cc=D[yy,x[1]];cc];
End[]
EndPackage[]

And suppose I do the following


<Diff[x[1]^2]


I expect to get 2x[1], but I get 0, what is going on? Probably I am missing something very simple. And yes I need variables in the form x[1],x[2],..., not x,y,z. Interestingly everything works perfectly fine if I do it without packaging:


Diff[yy_]:=Module[{cc},cc=D[yy,x[1]];cc];
Diff[x[1]^2]

The last operation gives 2x[1].



Answer



If you define Diff in a private context, like


BeginPackage["Diff`"]
Diff::usage = ""
Begin["`Private`"]

Diff[yy_] := Module[{cc}, cc = D[yy, x[1]]; cc];
End[]
EndPackage[]

then you will get


<< Diff`

Diff[x[1]^2]
(* 0 *)


That's because the x referred to in the package is in the Diff`Private` context:


Definition@Diff // InputForm
(* Diff[Diff`Private`yy_] := Module[{Diff`Private`cc}, 
Diff`Private`cc = D[Diff`Private`yy, Diff`Private`x[1]]; Diff`Private`cc] *)

and so it's not the same x that you are calling Diff with, which is in the Global context:


Context[x]
(* "Global`" *)

To solve this, you can declare the x in your package to be in the Diff` context like so:



BeginPackage["Diff`"]
Diff::usage = ""
x::usage = ""
Begin["`Private`"]
Diff[yy_] := Module[{cc}, cc = D[yy, x[1]]; cc];
End[]
EndPackage[]

Since Diff` is put on the $ContextPath by EndPackage, when you refer to x after loading the package, it is translated to Diff`x, which matches the definition in the package (Make sure you restart the kernel first, if you're following along):


<< Diff`


Diff[x[1]^2]
(* 2 x[1] *)

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