Symbolize Does Not Work in `.m` Files or What?

Question

I have a .nb (notebook) file which I should convert to a .m (mathematica package) file to run it remotely from command line of a high performance computing server. Before doing that I want to test whether my .m file runs correctly or not. (If I could run a .nb file using the command line then I didn't have all this trouble explained below!)

In my .nb file, I have used the Symbolize command for introducing the indexed symbols and I have used Save to get the output of the code in the format of a .m file. Everything works fine when I run the .nb file and the output is produced. Here is a simple code in a .nb file

Notice that the Symbolize is used from Notation palette and $x_1$ is entered as x + Ctrl + _ + 1. But when this is converted to a .m file (see this answer for converting .nb to .m), it turns into

ClearAll["Global`*"]
Needs["Notation`"]
Symbolize[ParsedBoxWrapper[SubscriptBox["x", "i_"]]]
Subscript[x, 1] = 1;
SetDirectory[NotebookDirectory[]];
Save["OutPut.m", Subscript[x, 1]]

and after running the .m file I get this error

which means that $x_1$ is not a symbol. According to the following code, I conclude that Symbolize is not working in a .m file or there is some problem in the conversion of .nb to .m!

What should I do to fix this? Specifically, what should I do so that after converting .nb to .m such errors do not come up?

Any help or suggestion is appreciated. :)

Answer 1

This answer may seem slightly off but it was posted before recent updates. The bottom line holds though.

It symbolizes boxes, not expressions, it is not Subscript which is now special but SubscriptBox.

You are supposed to use $x_1$ in your code but if you can't use StandardForm/2d typesetting then you have to make a round trip to boxes and back to expression:

roundtrip =  Function[expr
  , ToExpression@MakeBoxes[expr, StandardForm]
  , HoldFirst
];

roundtrip[ Subscript[x, 1] = 123 ]

roundtrip[ Save["OutPut.m", Subscript[x, 1]] ]

FilePrint@"OutPut.m"

Answer 2

The Notation package relies on Box Form as used by the Front End. Packages (generally) do not use Box Form therefore the Notation package does not work there. If you start WolframKernel.exe and evaluate Get["Notation`"] you will see a variety of error messages starting with:

FrontEndObject::notavail: A front end is not available; certain operations require a front end.

In translating from Box Form to plain text compromises have to be made as there is no direct equivalent for many things.

A Box Form subscript is normally translated as Subscript but this does not preserve the Symbol-like behavior enacted by the Notation package. If you need Symbol-like behavior then a different compromise will need to be made. One option is to replace the Subscript expression with a Symbol, which is what the Notation package is doing behind the scenes. So your package code would look like:

ClearAll["Global`*"]

x⎵Subscript⎵1 = 1;

SetDirectory[NotebookDirectory[]];

Save["OutPut.m", x⎵Subscript⎵1]

(When the Notation package is loaded and subscripts are Symbolized this is the translation made by ToString[expr, InputForm].)

If your package will be loaded from within the Front End then it is possible to load the Notation package. Since packages are not written in Box Form we will need to manually apply ToExpression to our lines of code. Your package might look like:

ClearAll["Global`*"]

Needs["Notation`"]

Symbolize[ParsedBoxWrapper[SubscriptBox["x", "i_"]]]

\(x\_1 = 1\) // ToExpression

\(Save[\("OutPut.m", x\_1\)]\) // ToExpression

This does work when loaded from a Notebook with Get, producing a file:

x\[UnderBracket]Subscript\[UnderBracket]1 = 1

Expressions may be converted into the shorthand box form (e.g. \(x\_1 = 1\)) using:

Function[, ToString[MakeBoxes @ #, InputForm], HoldAllComplete]