[Tex/LaTex] How to include Mathematica code in a document

wolfram-mathematica

I want to include some Mathematica code in a LaTeX document.

It's along the lines of
f[a_,b_]:=a^2+b^2+4b^3+25a*b*c ;

However, when I build my PDF, the _ and ^ always render. Is there a way to get it to just show up as it shows above?

Best Answer

As rdhs mentionned, you can use the listings package. A sample example is:

\documentclass{article}

\usepackage{listings}
\lstloadlanguages{[5.2]Mathematica}

\begin{document}

\begin{lstlisting}
f[a_,b_]:=a^2+b^2+4b^3+25a*b*c ;
\end{lstlisting}

For inline stuff you can use \lstinline$f[a_,b_]:=a^2+b^2+4b^3+25a*b*c ;$
 instead of the lstlisting environment. 
    \end{document}

Note the verb like delimiters for lstinline. One thing however, the listings manual indicates verb like delimiters, but in all of my work I use the usual { and } and it works fine (maybe a quirk, but I find it easier to read and will continue using it as long as possible)

enter image description here

There are other ways also. For example the minted package does what you what, but it requires that you install Pygments, which is a Python library.

Usage example

Print screen of result:

TeX code:

\documentclass{article}

\usepackage[margin=2cm]{geometry}
\usepackage[utf8]{inputenc}
\usepackage[T1]{fontenc}
\usepackage{lmodern}

\usepackage{mmacells}


\mmaDefineMathReplacement[≤]{<=}{\leq}
\mmaDefineMathReplacement[≥]{>=}{\geq}
\mmaDefineMathReplacement[≠]{!=}{\neq}
\mmaDefineMathReplacement[→]{->}{\to}[2]
\mmaDefineMathReplacement[⧴]{:>}{:\hspace{-.2em}\to}[2]
\mmaDefineMathReplacement{∉}{\notin}
\mmaDefineMathReplacement{∞}{\infty}
\mmaDefineMathReplacement{𝕕}{\mathbbm{d}}


\mmaSet{
  morefv={gobble=2},
  linklocaluri=mma/symbol/definition:#1,
  morecellgraphics={yoffset=1.9ex}
}


\begin{document}

Input from question with output from my Mathematica version.
Input is in input form, it can be copied and pasted to Mathematica.
\begin{mmaCell}[functionlocal=y]{Code}
  Integrate[{y^(-3)*(1-(a/y)^2)^(-2)},{y,r,Infinity}]
\end{mmaCell}
\begin{mmaCell}{Output}
  \{ConditionalExpression[-\mmaFrac{1}{2 (\mmaSup{a}{2} - \mmaSup{r}{2})},
     Im[r] Re[a] ≠ Im[a] Re[r] || ((a + r > 0 || a + r ∉ Reals) &&
       ((Re[a] < r && Im[a] == 0) || a - r ∉ Reals)) || r ∉ Reals]\}
\end{mmaCell}

For comparison, same cells obtained by including PDFs exported from Mathematica:
% You need inCell.pdf and outCell.pdf files for this to work.
% \mmaCellGraphics{Input}{inCell}
% \mmaCellGraphics[yoffset=3.5ex]{Output}{outCell}

Same input expression, but in standard form (as if it was inputted using math assistant). Note that syntax coloring still works.
\begin{mmaCell}[index=3,functionlocal=y]{Input}
  \mmaSubSupM{\int}{r}{∞}\{\mmaFrac{1}{\mmaSup{y}{3}\mmaSup{\big(1-\mmaSup{\big(\mmaFrac{a}{y}\big)}{2}\big)}{2}}\}𝕕y
\end{mmaCell}


More features:
\begin{mmaCell}[
  moredefined=f,
  functionlocal=a,
  local=b,
  pattern={x_,x},
  excessargument=n,
  linkbuiltin=List
]{Code}
  (* A (* nested *) comment. *)
  Block[{a=3},a+2]
  f[x_]:=2x+1 
  Module[{b=c},
      Print["a string \" with double quotes inside ", b/d];
      b+1
  ]
  f[z]//FullForm
  Sin[m,n]
  List[1,List[2,3]]; (* Links to documentation. *)
\end{mmaCell}
\begin{mmaCell}{Output}
  5
\end{mmaCell}
\begin{mmaCell}{Print}
  a string " with double quotes inside \mmaFrac{c}{d}
\end{mmaCell}
\begin{mmaCell}[addtoindex=1]{Output}
  1+c
\end{mmaCell}
\begin{mmaCell}[form=FullForm]{Output}
  Plus[1,Times[2,z]]
\end{mmaCell}
\begin{mmaCell}[messagelink={message/General/argx}]{Message}
  Sin::argx: Sin called with 2 arguments; 1 argument is expected. >>
\end{mmaCell}
\begin{mmaCell}{Output}
  Sin[m,n]
\end{mmaCell}
\begin{mmaCell}{Output}
  \{1,\{2,3\}\}
\end{mmaCell}
Graphics mixed with code:
\begin{mmaCell}{Code}
  a Graphics[{Green,Disk[]},ImageSize->50]/2
\end{mmaCell}
% You need greenDisk.pdf file for this to work.
% \begin{mmaCell}[moregraphics={moreig={scale=.7}}]{Output}
%   \mmaFrac{a \mmaGraphics{greenDisk}}{2}
% \end{mmaCell}
\begin{mmaCell}{Code}
  (* Different roles of one symbol. *)
  x;
  _x;
  \mmaDef{x_};
  \mmaPat{x_}->2x;
  \mmaPat{x_}:>2\mmaPat{x};
  f[\mmaPat{x_}]=2x;
  f[\mmaPat{x_}]:=2\mmaPat{x};
  Block[{\mmaFnc{x}},2\mmaFnc{x}];
  Module[{\mmaLoc{x}},2\mmaLoc{x}];
  \mmaUnd{Module}; (* undefined Module symbol *)
  \mmaLnB{Module}; (* Module symbol with link to documentation *)
  Sin[x\mmaExc{,x}];
\end{mmaCell}
\begin{mmaCell}[addtoindex=11]{Input}
  (* Nesting of "formatting boxes" *)
  \mmaSup{a}{\mmaSup{a}{a}} \mmaSub{a}{\mmaSub{a}{a}} \mmaSubSup{a}{\mmaSubSup{a}{a}{a}}{\mmaSubSup{a}{a}{a}} \mmaUnder{a}{\mmaUnder{a}{a}} \mmaOver{a}{\mmaOver{a}{a}} \mmaUnderOver{a}{\mmaUnderOver{a}{a}{a}}{\mmaUnderOver{a}{a}{a}} \mmaFrac{a}{\mmaFrac{a}{\mmaFrac{a}{a}}} \mmaSqrt{\mmaSqrt{a}} \mmaRadical{a}{\mmaRadical{a}{a}}
\end{mmaCell}
\begin{mmaCell}{Input}
  (* Replacements for infix operators in "Input" cells. *)
  x>=y; x<=y; x!=y; x->y; x:>y;
\end{mmaCell}
\begin{mmaCell}{Code}
  (* No replacement in "Code" cells. *)
  x>=y; x<=y; x!=y; x->y; x:>y;
\end{mmaCell}
\begin{mmaCell}[label={(\mmaCellIndex)custom}]{Code}
  (* Cell with custom label. *)
\end{mmaCell}
\begin{mmaCell}{Input}
  \mmaLnT{x}=2;(* labeled definition of x *)
\end{mmaCell}
\begin{mmaCell}{Input}
  \mmaLnL{x}(* usage of x with link to its definition *)
\end{mmaCell}

Implemented syntax elements:
\begin{mmaCell}[
  defined=defined,
  undefined=undefined,
  functionlocal=functionlocal,
  local=local,
  pattern=pattern,
  localconflict=localconflict,
  globalconflict=globalconflict,
  excessargument=excessargument,
  unknownoption=unknownoption,
  unwantedassignment=unwantedassignment,
  shadowing=shadowing,
  syntaxerror=syntaxerror,
  emphasizedsyntaxerror=emphasizedsyntaxerror,
  formattingerror=formattingerror,
]{Code}
  \mmaDef{Def} defined (*  defined symbol *)
  \mmaUnd{Und} undefined (* UndefinedSymbol *)
  \mmaFnc{Fnc} functionlocal (* FunctionLocalVariable *)
  \mmaLoc{Loc} local (* LocalVariable *)
  \mmaPat{Pat} pattern (* PatternVariable *)
  \mmaLCn{LCn} localconflict (* LocalScopeConflict *)
  \mmaGCn{GCn} globalconflict (* GlobalToLocalScopeConflict *)
  \mmaExc{Exc} excessargument (* ExcessArgument *)
  \mmaOpt{Opt} unknownoption (* UnknownOption *)
  \mmaAsg{Asg} unwantedassignment (* UnwantedAssignment *)
  \mmaShd{Shd} shadowing (* SymbolShadowing *)
  \mmaSnt{Snt} syntaxerror (* SyntaxError *)
  \mmaEmp{Emp} emphasizedsyntaxerror (* EmphasizedSyntaxError *)
  \mmaFmt{Fmt} formattingerror (* FormattingError *)
\end{mmaCell}

Inline cell: \mmaInlineCell[functionlocal=a]{Code}{Module[{a=5}, a]}.
Formatted inline cell:
\mmaInlineCell[pattern={x_,x}]{Input}{f[x_]:=\mmaFrac{\mmaSup{x}{2}}{5}}
\subsubsection*{
  Inline cell inside macro argument:
  \mmaInlineCellNonVerb[functionlocal=x]{Code}{Solve[\mmaSqrt{x}==y,x]}
}

\end{document}

Unicode

There are three strategies of handling Unicode supported by mmacells. Code for all of them can be automatically generated by CellsToTeX Mathematica package.

1. No Unicode

Don't use Unicode at all, use appropriate TeX commands instead. This approach works in all engines.

listings package doesn't color elements provided by escaped commands, so they need to be wrapped with appropriate annotations.

\documentclass{article}
\usepackage{mmacells}
\begin{document}

\begin{mmaCell}{Input}
\mmaSub{x}{1} == \mmaFrac{-\mmaUnd{\(\pmb{\beta}\)} \(\pmb{\pm}\) \mmaSqrt{\mmaSup{\mmaUnd{\(\pmb{\beta}\)}}{2} - 4 \mmaUnd{\(\pmb{\alpha}\)} \mmaUnd{\(\pmb{\gamma}\)}}}{2 \mmaUnd{\(\pmb{\alpha}\)}}
\end{mmaCell}

\end{document}

2. Unicode input

Use Unicode characters in input and automatically convert them to appropriate TeX commands by using \mmaDefineMathReplacement. This approach works in pdfTeX engine.

Replacements are implemented using listings literate option, so are "excluded" from automatic coloring, and identifiers containing Unicode characters need to be wrapped with appropriate annotations. Whether replacements will be used is controlled by mathreplacements option. By default Code cells don't use replacements (mathreplacements=none), Input cells use bold replacements (mathreplacements=bols) i.e. will use given command wrapped with math delimiters and \pmb, Output, Print and Message cells use "light" replacements (mathreplacements=light) i.e. will will use given command wrapped with math delimiters.

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{mmacells}
\begin{document}

\mmaDefineMathReplacement{±}{\pm}
\mmaDefineMathReplacement{α}{\alpha}
\mmaDefineMathReplacement{β}{\beta}
\mmaDefineMathReplacement{γ}{\gamma}

\begin{mmaCell}{Input}
\mmaSub{x}{1} == \mmaFrac{-\mmaUnd{β} ± \mmaSqrt{\mmaSup{\mmaUnd{β}}{2} - 4 \mmaUnd{α} \mmaUnd{γ}}}{2 \mmaUnd{α}}
\end{mmaCell}

\end{document}

3. Unicode input and output

Use Unicode characters in input and rely on appropriate glyphs of used fonts. This approach works in Unicode-aware engines.

Since listings does not support Unicode, it needs to be switched off using uselistings=false option. With listings switched off no automatic coloring occurs, so all identifiers, also those not containing Unicode characters, need to be wrapped with appropriate annotations.

\documentclass{article}
\usepackage{fontspec}
\usepackage{mmacells}

\setmainfont{FreeSerif}
\setmonofont{FreeMono}

\mmaSet{uselistings=false}

\begin{document}

\begin{mmaCell}{Input}
\mmaSub{\mmaUnd{x}}{1} == \mmaFrac{-\mmaUnd{β} ± \mmaSqrt{\mmaSup{\mmaUnd{β}}{2} - 4 \mmaUnd{α} \mmaUnd{γ}}}{2 \mmaUnd{α}}
\end{mmaCell}

\end{document}

[Tex/LaTex] Mathematica notebook into latex document

In terms of the equation positioning, I've added the fleqn option to the document class, but apart from that, the following is the only additions to the preamble to format the document contents:

% New stuff
\usepackage{environ}
\renewcommand{\pmb}[1]{#1}% Remove bold math
\RenewEnviron{doublespace}{%
  \let\noindent\relax%
  \let\(\relax\let\)\relax%
  \[\BODY\]
}

\let\oldtext\text
\renewcommand{\text}[1]{%
  \ifnum\pdfstrcmp{#1}{Sin}=0
    \cos
  \else\ifnum\pdfstrcmp{#1}{Cos}=0
    \sin
  \else\ifnum\pdfstrcmp{#1}{Tan}=0
    \tan
  \else\ifnum\pdfstrcmp{#1}{==}=0
    \equiv
  \else
    \oldtext{#1}
  \fi\fi\fi\fi
}

The intent is to

remove the use of \pmb in math context, since I don't know what it would be used for;
remove the doublespace environment's use as a display math equation. Instead, remove the use of \noindent, \( and \) and rather set the contents inside \[...\];
update \text to condition on its argument, thereby replacing \text{Cos} by \cos, as well as other possible constructions.

This is for sure not perfect, and could be improved. I also assumed that the superfluous spacing inside sectional titles is due to the author adding them, and should be removed manually.

Here's a complete translation of the document: