How to convert formal symbols to standard ones in an expression?

Question

Mathematica generates an expression sometimes using \[Formal] symbols. This is causing a problem with the TeXForm code generated as $\LaTeX$ is not able to process it. To clarify: The generated TeXForm should not include Unicode. The problem is that these are causing problem. So the solution should be such that, the result of applying TeXForm to the expression, should not produce Unicode.

Is there a way to make these expressions use normal symbols (normal x and y) so that I can generate $\LaTeX$ code from them that will work in my $\LaTeX$ document

 f = DifferentialRoot[Function[{y, x}, {y''[x] + y[x] == 0, y[0] == 0, y'[0] == 1}]]

If I do TeXForm[f] on the above, the $\LaTeX$ code generated is not valid with TeXLive. I just need the expression f not to contain those dots above and below the symbols. Just normal symbols. One way is to use

f = DifferentialRoot[Function[{y, x}, {y''[x] + y[x] == 0, y[0] == 0, y'[0] == 1}]]
    // OutputForm

which $\LaTeX$ can handle after TeXForm is applied to the above. But it will be nice to have x and y there instead.

Answer 1

Interesting question with more complications than I anticipated.

If it is not necessary to replace every formal Symbol with the equivalent plain version, but instead arbitrarily with specified Symbols, you can use something like this:

SetAttributes[formalQ, HoldFirst]
formalQ[s_Symbol] := StringMatchQ[ToString@HoldForm@FullForm@s, "\\[Formal*]"]

expr = DifferentialRoot[Function[{y, x}, {y''[x] + y[x] == 0, y[0] == 0, y'[0] == 1}]];

rep = {a, b, c, d, e};  (* new Symbols to use *)

old = Union @ Cases[expr, _Symbol?formalQ, {-1}]
new = Take[rep, Length @ old]
HoldForm @@ {expr} /. Thread[old -> new]

DifferentialRoot[Function[{b,a},{b[a]+(b^\[Prime]\[Prime])[a]==0,b[0]==0,(b^\[Prime])[0]==1}]]

Note that I had to wrap expr in HoldForm as otherwise it automatically puts the Formal Symbols right back!

I am still working on the larger problem of replacing every Formal Symbol with its plain equivalent.
If I cannot find an internal look-up table I may have to build my own.

If you are only dealing with automatically-generated Formal Symbols you may only have a few to replace:

Holonomic`$DifferenceRootFormalSymbols

Holonomic`$DifferentialRootFormalSymbols

{\[FormalY], \[FormalN]}

{\[FormalY], \[FormalX]}

Therefore I would start with:

fix = {\[FormalY] :> y, \[FormalN] :> n, \[FormalX] :> x}