Customize the TeXForm of D and Integrate

Question

Goal

Let the TeXForm of D and Integrate more pretty.

D[f[x], x] // HoldForm // TeXForm
D[f[x], {x, n}] // HoldForm // TeXForm
Integrate[f[x], {x, 0, Infinity}] // HoldForm // TeXForm
Integrate[f[x, y], x, y] // HoldForm // TeXForm

\begin{array}{*3{>{\displaystyle}l}} \text{Mathematica} & \LaTeX&\texttt{Problem}\\ \displaystyle\frac{\partial f(x)}{\partial x} & \displaystyle\frac{\mathrm{d}}{\mathrm{d}x}f(x)&\texttt{don't use \partial}\\ \displaystyle\frac {\partial^nf (x)} {\partial x^n} & \displaystyle\frac{\mathrm{d}^n}{\mathrm{d}x^n}f(x)&\texttt{don't put on numerator}\\ \displaystyle\int_0^{\infty } f(x) \, dx& \displaystyle\int_0^{\infty } f(x) \,\mathrm{d}x&\texttt{use\mathrm{d}}\\ \displaystyle\int \int f(x,y)dydx& \displaystyle\iint f(x,y)\,\mathrm{d}y\,\mathrm{d}x&\texttt{use\iint and why\,lost}\\ \end{array}

---

I tried @jkuczm 's TeXUtilities package.

Unprotect[Integrate,D];
Format[Integrate[fun__,x_],TeXForm]:=TeXDelimited["\\int{",fun,"\\,\\mathrm{d} ",x,"\\right)","DelimSeparator"->""];
Format[D[fun__,x_],TeXForm]:=TeXDelimited["\frac{\mathrm{d}}{\mathrm{d} ,"x ",},"fun,"DelimSeparator"->""];
Protect[Integrate,D];

Nothing happened, can't figure out how to use that.

Answer 1

We must remember to use HoldPattern to prevent evaluation of D[...] expression used on left hand side of definition. To make D formatting general we need some preprocessing of variable specification arguments to count total order of derivative.

Import@"https://raw.githubusercontent.com/jkuczm/MathematicaTeXUtilities/master/NoInstall.m"

Unprotect@D;
Format[HoldPattern@D[f_, vars__, OptionsPattern[]], TeXForm] := Module[{n = 0, v},
  v = Replace[HoldComplete@vars, {
    {x_, i_, ___} /; (n += i; True) :> HoldForm@HoldForm[x]^i,
    x_ /; (n++; True) :> HoldForm@HoldForm[x]
  }, {1}];
  TeXDelimited[
    "\\frac{" <> ToString[TeXVerbatim@"\\mathrm{d}"^n, TeXForm] <> "}{",
    Sequence @@ v,
    "} " <> ToString[Unevaluated@f, TeXForm],
    "BodyConverter" -> ("\\mathrm{d}" <> ToString[#, TeXForm]&),
    "BodySeparator" -> " \\, ",
    "DelimSeparator" -> ""
  ]
]
Protect@D;

Basic example:

D[f[x], x] // HoldForm // TeXForm
(* \frac{\mathrm{d}}{\mathrm{d}x} f(x) *)

$\frac{\mathrm{d}}{\mathrm{d}x} f(x)$

Complicated example with variables with assigned values to test potential evaluation leaks:

x = 10; y = 20; f = Plus;
D[f[x, y, z], {x, n}, y, {z, 2 + m}] // HoldForm // TeXForm
ClearAll[x, y, f]
(* \frac{\mathrm{d}^{3+m+n}}{\mathrm{d}x^n \, \mathrm{d}y \, \mathrm{d}z^{2+m}} f(x,y,z) *)

$\frac{\mathrm{d}^{3+m+n}}{\mathrm{d}x^n \, \mathrm{d}y \, \mathrm{d}z^{2+m}} f(x,y,z)$

---

For Integrate we must make sure that our custom format value takes precedence over built-in formatting, so we move it to beginning of FormatValues. Here I'll limit custom formatting to indefinite integrals with up to four variables, but of course more general rules can be defined.

Unprotect@Integrate;
Format[Integrate[fun_, vars : Repeated[_Symbol, {1, 4}]], TeXForm] := With[
  {v = HoldForm /@ HoldForm /@ HoldComplete@vars},
  TeXDelimited[
    "\\" <> StringRepeat["i", Length@v] <> "nt",
    Unevaluated@fun,
    Sequence @@ v,
    "",
    "DelimSeparator" -> " ",
    "BodySeparator" -> " \\, \\mathrm{d}"
  ]
]
(* Move TeXForm format to begining of FormatValues so they take precedence over existing ones. *)
FormatValues@Integrate = Join[#@False, #@True]&@GroupBy[FormatValues@Integrate, FreeQ@TeXForm];
Protect@Integrate;

Basic example:

Integrate[f[x], x] // TeXForm
(* \int f(x) \, \mathrm{d}x *)

$\int f(x) \, \mathrm{d}x$

Complicated example with variables with assigned values to test potential evaluation leaks:

x = 10; y = 20; f = Plus;
Integrate[f[x, y, z], x, y, z] // HoldForm // TeXForm
ClearAll[x, y, f]
(* \iiint f(x,y,z) \, \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z *)

$\iiint f(x,y,z) \, \mathrm{d}x \, \mathrm{d}y \, \mathrm{d}z$