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I'm used to pressing Ctrl+Shift+I (or N if I want a shorter form) to reformat my input cells in a nicer way after editing them, e.g., to remove unnecessary parentheses, add or remove spaces as needed, etc.

The issue comes when I define a custom output format for some expression. For example, let's say that I'm working with indexed variables of the form a[i, j]. It's easier to use, for example because I can just match patterns with things like _a. However, it is visually more pleasing to view such a variable as Subscript[a, i, j] in the output of a computation, because (among other things) that's what I actually write on my piece of paper when doing the math myself.

I know how to define an output format that takes care of the visual aspect:

Format[a[i_, j_]] := Subscript[a, i, j] a[1, 2] + a[2, 3] (* will display as expected *)

However, if I then use Ctrl+Shift+I on a cell that contains a[1,2], the expression will turn into Subscript[a, 1, 2], with no turning back.

Some options I'm aware of:

  • Use the Notation package. But it seems heavy weight, and if I want to avoid breaking Ctrl+Shift+N, I need to define two-way notation, which could be undesirable.
  • Define a format function like format[expr_] := expr /. a[i_, j_] :> Subscript[a, i, j] and then set $Post = format. But then, this runs every single time I get an output, and I'm afraid the ReplaceAll will get slow on large expressions, or if I start having more custom notation.

Any ideas?

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You need MakeBoxes+TemplateBox:

MakeBoxes[a[i_, j_], StandardForm] ^:= TemplateBox[MakeBoxes /@ {i, j}, "a", DisplayFunction -> (SubscriptBox["a", RowBox[{#, ",", #2}]] &)]

enter image description here

In Comparison with Notation Method

It's worth pointing out the effect of the method above is different from the two way notation of Notation package:

<< Notation` Notation[ParsedBoxWrapper[ SubscriptBox["a", RowBox[{"i_", ",", "j_"}]]] \[DoubleLongLeftRightArrow] ParsedBoxWrapper[RowBox[{"a", "[", RowBox[{"i_", ",", "j_"}], "]"}]]]

enter image description here

As we can see, the Subscript has been hajacked by Notation package. Once a 2D $a_{i,j}$ is created in the notebook, it'll be interpreted as a[i, j]. (Things like expr defined by expr = Subscript[a, 1, 2] won't be influenced, though. )

On the contrary, the MakeBoxes+TemplateBox has just created something looks exactly the same as Subscript[…]. Subscript won't be influenced:

enter image description here

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  • $\begingroup$ Thanks! That works nicely. How does this compare to the Notation package? $\endgroup$ Commented May 11, 2024 at 13:49
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    $\begingroup$ @NajibIdrissi Just as you've noticed :) . 1. We don't need to load the package so it's light-weighted. 2. It's actually different from the two way notation of Notation package. Once we define a two way notation with Notation package, all the $a_{i,j}$ will be treated as a[i,j] even if we manually input a, Ctrl+-,i,j or Subscript[a, i, j]. But using my method, a, Ctrl+-,i,j or Subscript[a, i, j] will still be interpreted as Subscript[a, i, j]. In other words, my method doesn't hijack Subscript, it only creates something looks exactly the same as Subscript. $\endgroup$ Commented May 11, 2024 at 15:44
  • $\begingroup$ @NajibIdrissi I've elaborated a bit with 2 GIFs, see my update. $\endgroup$ Commented May 11, 2024 at 16:07
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    $\begingroup$ BTW, though not quite related to your question, you may want to read this to learn what Notation package actually does: mathematica.stackexchange.com/a/185475/1871 @NajibIdrissi $\endgroup$ Commented May 11, 2024 at 16:18

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