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I used the Notation package to symbolize expressions of the form Superscript[u,_]. I then proceeded to manually input the values of various $u^x$ where $x$ varies in L={a,b,c,d,...}. How can I define a function that takes an element $x$ in L and outputs the value of $u^x$? I've tried doing something like

F[x_]:=Superscript[u,x]

but whenever I evaluate it I just get $u^x$ (i.e. F[a] outputs Superscript[u,x]). I also tried composing with ToExpression and many other functions but they don't seem to work.

Edit: The reason as to why I'm using the Notation package is because I want to set expressions like this:

enter image description here

where I later set the values of each block and then perform operations with $w^{A,B}$.

Julio Cáceres
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    Input $u^x$ manually and press Ctrl+Shift+I and observe, then you'll probably know what to do. (Well, but why are you using Notation\`` package if you need theSuperscript` be "alive"? ) – xzczd Aug 12 '23 at 00:17
  • What do you mean by "alive"? I'm using the Notation package to make the notebook more readable. In reality I'm manually setting the values of multiple matrices $u^{x,y}$, each of which consists of blocks $u^{x,y}_{z,w}$. I'd like to find a way to verify some properties for all these matrices without having to manually check each one. Using Ctrl+Shift+I only turned $u^x$ into u\[UnderBracket]Superscript\[UnderBracket]x. – Julio Cáceres Aug 12 '23 at 00:46
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    I mean, by default the u and x in Superscript is separated i.e. you can do something like Superscript[u, x]/. x->aa to obtain Superscript[u, aa], but Notation\`` package will transform it tou[UnderBracket]Superscript[UnderBracket]xthat is a single symbol and you won't be able to make replacement easily anymore. "I'm using the Notation package to make the notebook more readable." I don't understand,StandardFormofSuperscriptis already 2D, why do you needNotation`` package? – xzczd Aug 12 '23 at 01:05
  • I just added a picture explaining why I feel like I need the Notation package. – Julio Cáceres Aug 12 '23 at 01:51
  • The answers in that other questions helped me a lot. I added a new shortcut Superscript and will be using that to input my values, it is clunky at times though. You can post your last comment as an answer to accept. – Julio Cáceres Aug 12 '23 at 04:08
  • When writing my (now removed) last comment I didn't notice you've actually mixed up Superscript and Power. Please see the revised answer below for more info. – xzczd Aug 13 '23 at 05:06

1 Answers1

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First of all, you've mixed up Superscript and Power. Though the 2D form (to be more precise, StandardForm) of them looks the same, they are totally different. When one presses Ctrl+6, the 2D form of Power will be created. According to the mentioned behaviors (InputForm of your symbolized $u^x$ is u⎵Superscript⎵x, Set::write warning in picture, etc.), what you've really done is inputting 2D Power rather than Superscript.

Symbolizing the 2D Power[…, …] is a bad idea in my view, because:

  1. Power is so frequently used, symbolizing it will probably cause other trouble.

  2. The superscript in symbolized Power cannot be modified in a simple manner. (Actually avoiding undesired modification of subscript/superscript/… is one of the main purposes of using Notation` package. ) But you need to modify the superscript.

Since what you really need is just avoiding Set::write and manipulating the superscript later, using Superscript instead of Power should be the way to go. To input Superscript easily, the solutions in the following post should help:

Preventing Superscript from being interpreted as Power when using Ctrl+^ shortcut?

Finally, though the original question has now been proved to be a XY problem, let me show a solution anyway:

<< Notation`

Symbolize@ParsedBoxWrapper@SuperscriptBox["v", "_"]
(* Notice it's important to use 1D Power[…, …] in the following line *)
G[x_] := ToExpression@MakeBoxes@Power[v, x]


G[a] /. a -> b


(* v⎵Superscript⎵a *)

enter image description here

This solution works because Notation` is essentially a package that influences the transformation between boxes and expressions, so we can call the transformation rule created by Symbolize programmatically with MakeBoxes and ToExpression.

xzczd
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