Let's take a composite Mathematica command:
A[B[]]
where A and B - two arbitrary Mathematica commands and [] - inner object of arbitrary structure
What code to use to swap them, i.e.:
A[B[]]$\xrightarrow{\text{?}}$B[A[]]
for example:
D[Sin[]]$\xrightarrow{\text{?}}$Sin[D[]]
Let's also consider a more complicated case:
for expression D[Transpose[x] + Sin[x y], x]
we must get Transpose[D[x, x]] + Sin[D[x y, x]]
D is the derivative operator in MMA. Therefore, I am using DD.
You may achieve your goal using "ReplaceAll" with the following pattern:
pat= x1_[x2_[x3_]] -> x2[x1[x3]]
With this, e.g.:
DD[Sin[a]] /. pat
(* Sin[DD[a]] *)
D command, I need to use Unprotect and Protect? It all boils down to working with the rules one way or another... It would be interesting to try some alternatives. Is it possible to avoid the removal of protection from the D command?
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D, or are you saying that D just happens to be one of the heads you want to swap with? If the latter, then it gets more complicated, because D expects more than one argument.
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D expects more than one argument." Actually D[a] returns a, this is a surprisng hidden syntax :) . You may want to read this: mathematica.stackexchange.com/a/163273/1871
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D[Transpose[x] + Sin[x y], x], and the desired result should look like Transpose[D[x, x]] + Sin[D[x y, x]]
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