String replacement to make the TeXForm output beautiful

Question

This question is inspired by this question: How to convert the symbol $d$ in Integrate into $\mathrm{d}$?.

Although it’s not a big problem, the TeXForm can be modified manually to “standard” form, I’m curious why Mathematica’s TeXForm won’t change the differential d to $\mathrm{d}$ automatically.

There are some detailed situations to pay attention to.

• The integrand or the integration argument may contain some variables having letter “d”(Such as: det, adcda, etc.) or even “d” itself.(Although it’s ugly to do so.)

• Mathematica will automatically change alpha to $\alpha$.

• Single-character symbol names are given in italic font, while multiple character names are given in roman font.

I’ve written some lines of codes to do this. But I think the code is ugly and can’t handle the situation with integration argument’s name exactly “d”. Here is my code.

cTeXForm[expr_, arg__] := Module[{
  (*temp saves the original TeXForm*)
  temp = ToString@TeXForm@HoldForm[Integrate[expr, arg]],
 (*var saves the integration argument and reverse the order to keep up with the integral symbol*)
  var = ToString /@ TeXForm /@ Reverse@(Flatten /@ ({#} & /@ {arg}))[[;; , 1]], pos, range, betweenQ, loc},
  (*locate the position of differential d*)
  pos = StringPosition[temp, "d"][[;; , 1]];
  range = StringPosition[temp, var];
  betweenQ[n_] := Catch@(Scan[If[#[[1]] <= n <= #[[2]], Throw[0], n] &, range];Throw[1]);
  loc = {#, #} & /@ 
  Pick[pos, betweenQ[#] & /@ pos, 1][[-Length@var ;; -1]] ;
  (*replace and output*)
  CopyToClipboard@OutputForm@StringReplacePart[temp, "\\mathrm{d}", loc]]

Here is the test (although no beautiful):

cTeXForm[x^2 alpha d baded, {x, 1, 2}, {alpha, 2, 3},baded]

And here is the output of my code

$$\int _1^2\int _2^3\int \alpha \text{baded} d x^2\mathrm{d}\text{baded}\mathrm{d}\alpha \mathrm{d}x$$

So the question is how to precisely change the differential d to $\mathrm{d}$? Are there any other ways to do this? (RegularExpression, rule-based replacement etc. I’m not familiar with these.)

Any advice about the string manipulation or using TeXForm is welcomed.

Answer 1

I think I've found an answer to my own question.

Bypassing the difficulties of replacing d to $\mathrm{d}$, the following code constructs the intended TeX-form directly.

SetAttributes[integralTeXForm, HoldAll]
integralTeXForm[expr_, arg__] := Module[{temp, var, add},
  add = If[Length@# == 3, "_" <> #[[2]] <> "^" <> #[[3]] <> " ", ""] &;
  temp = ToString@TeXForm@HoldForm[expr];
  var = Map[ToString@TeXForm@# &, Reverse@(Flatten /@ ({#} & /@ {arg})), {2}];
  CopyToClipboard@Fold["\\int " <> add[#2] <> #1 <> "\\,\\mathrm{d}" <> #2[[1]]&, temp, var]
]

And the code above can also maintain the order of variables in the integrand.