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Suppose I have a function of the form $ a_1 a_2 \cdots a_n b_1 \cdots b_m \cdots f[L[x,y]]$. I want to make some particular letters and their power inside the bracket.

i.e., I want the letter $\alpha, \beta$ be inside the bracket \begin{align} X * \alpha^{m} *\beta^{n} f[A[x,y]] \Rightarrow X f[\alpha^{m}\beta^{n} A[x,y]] \end{align} What I know for the include of function in general is the following :

 a*f[L[x, y]] /. {A_ f[x__] -> f[A*x]}

but this does not specify the certain conditions for my purpose. i.e., for Xaf[L[x,y]] it just gives f[a X L[x,y]]$.

Specifically what I want to do is for some specific powers of letters $X*\alpha^{m}*\beta^{n}*\gamma^{l}*\delta^{e} f[A[x,y]]$ I want to pick some letter, i.e. ,$\alpha, \beta$, and include this the function $f$, i.e. ,I want my result be $X \gamma^{l} \delta^{e} f[ \alpha^{m} \beta^{n} A[x,y]]$

Without explicit substitution case by case, are there a nice way to implement this by mathematica?

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1 Answer 1

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$Version

(* "13.3.1 for Mac OS X ARM (64-bit) (July 24, 2023)" *)

Clear["Global`*"]

rule = {(A : _?(! FreeQ[#, a | b] &) : 1)*
  (B : _?(FreeQ[#, a | b] &) : 1)*f[x__] -> B*f[A*x]};

test = {X f[L[x, y]], a*f[L[x, y]], a*X*f[L[x, y]], b^n*X*f[L[x, y]], 
   a^m*b*X*f[L[x, y]], a^m*b^n*X*f[L[x, y]]};

Transpose[{test, test /. rule}] // Column

enter image description here

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  • $\begingroup$ if I want to include $c$ or $d$ in the rule, what should I modify? $\endgroup$
    – phy_math
    Dec 5, 2023 at 7:03
  • $\begingroup$ Look at the documentation for Alternatives, it can take as many arguments as you want. $\endgroup$
    – Bob Hanlon
    Dec 5, 2023 at 7:58

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