Display Conjugate[x_] as a long overbar permanently

Question

In TraditionalForm output, I would like to have Conjugate be always displayed as an overbar, not an asterisk superscript. In particular for complicated expressions like Conjugate[Log[z]], I would like to have a long overbar.

There are various solutions proposed in other threads, including the simplest version:

Unprotect[Conjugate];
Format[Conjugate[x_], TraditionalForm] := OverBar@Pane@x;
Protect[Conjugate];

This gives the desired result, but only the first time I call // TraditionalForm on some output.

How can I ensure that this new format rule is applied throughout the rest of my notebook?

PS: As requested here a full MWE with Mathematica 13.0.1.0.

Quit[];
Unprotect[Conjugate];
Format[Conjugate[x_], TraditionalForm] := OverBar@Pane@x;
Protect[Conjugate];
Conjugate[Log[z]] // TraditionalForm
Conjugate[Log[z]] // TraditionalForm

I obtain the output

$\overline{\log z}$

$(\log z)^*$

Answer 1

You are encountering two issues.

1. Conjugate is a symbol which autoloads definitions when it is used or displayed.
2. The autoloaded definitions use Condition, making it difficult to force your new definition to be favored.

I recommend using my Initial function to solve these issues, which I repeat here for convenience:

Initial /: Verbatim[TagSetDelayed][Initial[sym_], lhs_, rhs_] := With[
    {
    new = Block[{sym},
        TagSetDelayed[sym, lhs, rhs];
        First@Language`ExtendedDefinition[sym, "ExcludedContexts" -> {}]
    ],
    protect=Unprotect[sym]
    },

    (* Force autoloading of sym *)
    sym;
    Quiet@MakeBoxes[sym[],TraditionalForm];

    (* Autloading can cause a symbol to become protected *)
    Unprotect[sym];

    (* Insert new values in front *)
    Replace[
        new,
        Rule[values_, n_] :> insertValues[n, values, sym],
        {2}
    ];
    Protect@protect;
]

insertValues[n_, v_, sym_] := If[n =!= {},
    v[sym] = DeleteDuplicatesBy[
        Join[n, v[sym]],
        equivalenceClass
    ]
]

equivalenceClass[lhs_ :> rhs_] := If[FreeQ[Hold[rhs], Condition],
    lhs,
    lhs :> rhs
]

Then, you can make your new definition with:

Initial[Conjugate] /: Format[Conjugate[x_], TraditionalForm] := OverBar @ Pane @ x

and you should get your desired behavior.

Update

If you really want the argument to be parenthesized (it seems unnecessary to me), then you could do:

Initial[Conjugate] /: MakeBoxes[Conjugate[x_], TraditionalForm] := TemplateBox[
    {Parenthesize[x, TraditionalForm, Power, Left]},
    "Conjugate",
    DisplayFunction -> Function@OverscriptBox[PaneBox@#,"_"]
]

Answer 2

You can deal with it through stylesheets, which may or may not be convenient for you. You can set up a stylesheet for your notebooks or execute this:

SetOptions[EvaluationNotebook[], 
 StyleDefinitions -> 
  Notebook[{Cell[StyleData[StyleDefinitions -> "Default.nb"]], 
    Cell[StyleData["Conjugate"], 
     TemplateBoxOptions -> {DisplayFunction -> (OverscriptBox[
           PaneBox[#1], 
           StyleBox["_", FontFamily -> "Times", 
            SingleLetterItalics -> False]] &), 
       Tooltip -> Automatic}]}]]

Note the TemplateBoxOptions must be set for the style "Conjugate" for this to work.

Answer 3

So I tracked the difference between TraditionalForm and DisplayForm to use of TemplateBox. Answer of @Michael E2 is really good, however a more minimal override may be written:

Unprotect[TemplateBox];
TemplateBox[x_, "Conjugate", SyntaxForm -> SuperscriptBox] := 
 OverscriptBox[x[[1]], "_"]
Protect[TemplateBox];

I tested on following input:

Conjugate[c] // TraditionalForm
Conjugate[Log[z]] // TraditionalForm
Conjugate[Log[z]] // TraditionalForm

No nasty stars attached.

Answer 4

This thing is usually done with Format function definition. However Conjugate as a built-in is protected. The code snippet to do that is

Unprotect[Conjugate]
Format[Conjugate[a_],StandardForm]:= OverBar[a]
Protect[Conjugate]

where the last line is optional. Works quite all right.

Answer 5

The final solution I used is a slight modification of @fqrt's answer using a TemplateBox below, but introducing an additional PaneBox:

Unprotect[TemplateBox];
TemplateBox[x_, "Conjugate", SyntaxForm -> SuperscriptBox] := OverscriptBox[PaneBox[x[[1]], ImageMargins -> 1], "_"];
Protect[TemplateBox];