path: root/macros/latex/contrib/sagetex/py-and-sty.dtx

% \section{Implementation}
% \label{sec:implementation}
%
% There are two pieces to this package: a \LTX style file, and a
% Python module. They are mutually interdependent, so it makes sense to
% document them both here.
%
% \subsection{The style file}
% \label{sec:sty-file}
%
% \iffalse
% tell docstrip to put code into the .sty file
%<*latex>
% \fi
%
% All macros and counters intended for use internal to this package
% begin with ``|ST@|''.
%
% \subsubsection{Initialization}
%
% Let's begin by loading some packages. The key bits of |sageblock| and
% friends are stol---um, adapted from the |verbatim| package manual. So
% grab the |verbatim| package. We also need the |fancyvrb| package for
% the |sageexample| environment
%    \begin{macrocode}
\RequirePackage{verbatim}
\RequirePackage{fancyvrb}
%    \end{macrocode}
% and |listings| for the |sagecommandline| environment.
%    \begin{macrocode}
\RequirePackage{listings}
\RequirePackage{xcolor}
\lstdefinelanguage{Sage}[]{Python}
  {morekeywords={False,sage,True},sensitive=true}
\lstdefinelanguage{SageOutput}[]{}
  {morekeywords={False,True},sensitive=true}
\lstdefinestyle{DefaultSageInputOutput}{
  nolol,
  identifierstyle=,
  name=sagecommandline,
  xleftmargin=5pt,
  numbersep=5pt,
  aboveskip=0pt,
  belowskip=0pt,
  breaklines=true,
  numberstyle=\footnotesize,
  numbers=right
}
\lstdefinestyle{DefaultSageInput}{
  language=Sage,
  style=DefaultSageInputOutput,
  basicstyle={\ttfamily\bfseries},
  commentstyle={\ttfamily\color{dgreencolor}},
  keywordstyle={\ttfamily\color{dbluecolor}\bfseries},
  stringstyle={\ttfamily\color{dgraycolor}\bfseries},
}
\lstdefinestyle{DefaultSageOutput}{
  language=SageOutput,
  style=DefaultSageInputOutput,
  basicstyle={\ttfamily},
  commentstyle={\ttfamily\color{dgreencolor}},
  keywordstyle={\ttfamily\color{dbluecolor}},
  stringstyle={\ttfamily\color{dgraycolor}},
}
\lstdefinestyle{SageInput}{
  style=DefaultSageInput,
}
\lstdefinestyle{SageOutput}{
  style=DefaultSageOutput,
}
\providecolor{dbluecolor}{rgb}{0.01,0.02,0.7}
\providecolor{dgreencolor}{rgb}{0.2,0.4,0.0}
\providecolor{dgraycolor}{rgb}{0.30,0.3,0.30}
%    \end{macrocode}
% Unsurprisingly, the |\sageplot| command works poorly without graphics
% support.
%    \begin{macrocode}
\RequirePackage{graphicx}
%    \end{macrocode}
% The |makecmds| package gives us a |\provideenvironment| which we need,
% and we use |ifpdf| and |ifthen| in |\sageplot| so we know what kind of
% files to look for. Since |ifpdf| doesn't detect running under XeTeX
% (which defaults to producing PDFs), we need |ifxetex|. Hopefully the
% |ifpdf| package will get support for this and we can drop |ifxetex|.
% We also work around ancient \TeX{} distributions that don't have
% |ifxetex| and assume that they don't have XeTeX.
%    \begin{macrocode}
\RequirePackage{makecmds}
\RequirePackage{ifpdf}
\RequirePackage{ifthen}
\IfFileExists{ifxetex.sty}{
  \RequirePackage{ifxetex}
}{
  \newboolean{xetex}
  \setboolean{xetex}{false}}
%    \end{macrocode}
%
% Next set up the counters, default indent, and flags.
%    \begin{macrocode}
\newcounter{ST@inline}
\newcounter{ST@plot}
\newcounter{ST@cmdline}
\setcounter{ST@inline}{0}
\setcounter{ST@plot}{0}
\setcounter{ST@cmdline}{0}
\newlength{\sagetexindent}
\setlength{\sagetexindent}{5ex}
\newif\ifST@paused
\ST@pausedfalse
%    \end{macrocode}
% Set up the file stuff, which will get run at the beginning of the
% document, after we know what's happening with the |final| option.
% First, we open the |.sage| file:
%    \begin{macrocode}
\AtBeginDocument{\@ifundefined{ST@final}{%
\newwrite\ST@sf%
\immediate\openout\ST@sf=\jobname.sagetex.sage%
%    \end{macrocode}
% \begin{macro}{\ST@wsf}
%   We will write a lot of stuff to that file, so make a convenient
%   abbreviation, then use it to put the initial commands into the
%   |.sage| file. The hash mark below gets doubled when written to the
%   file, for some obscure reason related to parameter expansion. It's
%   valid Python, though, so I haven't bothered figuring out how to get
%   a single hash. We are assuming that the extension is |.tex|; see the
%   |initplot| documentation on page~\pageref{initplot} for discussion
%   of file extensions. (There is now the \texttt{currfile} package
%   (\url{http://www.ctan.org/pkg/currfile/}) which can figure out file
%   extensions, apparently.) The ``|(\jobname.sagetex.sage)|'' business
%   is there because the comment below will get pulled into the
%   autogenerated |.py| file (second order autogeneration!) and I'd like
%   to reduce possible confusion if someone is looking around in those
%   files. Finally, we check for version mismatch and bail if the .py
%   and .sty versions don't match and the user hasn't disabled checking.
%   Note that we use |^^J| and not |^^J%| when we need indented lines.
%   Also, |sagetex.py| now includes a |version| variable which
%   eliminates all the irritating string munging below, and later we can
%   remove this stuff and just use |sagetex.version|.
%   \changes{v2.2.4}{2010/02/15}{Add version mismatch checking.}
%   \changes{v2.3.3}{2012/01/13}{Improve version mismatch checking,
%   include Mercurial revision in version string.}
%    \begin{macrocode}
\newcommand{\ST@wsf}[1]{\immediate\write\ST@sf{#1}}%
\ST@wsf{%
# -*- encoding: utf-8 -*-^^J%
# This file (\jobname.sagetex.sage) was *autogenerated* from \jobname.tex with
sagetex.sty version \ST@ver.^^J%
import sagetex^^J%
_st_ = sagetex.SageTeXProcessor('\jobname', version='\ST@ver', version_check=\ST@versioncheck)}}%
%    \end{macrocode}
% On the other hand, if the |ST@final| flag is set, don't bother with
% any of the file stuff, and make |\ST@wsf| a no-op.
%    \begin{macrocode}
{\newcommand{\ST@wsf}[1]{\relax}}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\ST@dodfsetup}
%   The |sageexample| environment writes stuff out to a different file
%   formatted so that one can run doctests on it. We define a macro that
%   only sets this up if necessary.
%    \begin{macrocode}
\newcommand{\ST@dodfsetup}{%
\@ifundefined{ST@diddfsetup}{%
\newwrite\ST@df%
\immediate\openout\ST@df=\jobname_doctest.sage%
\immediate\write\ST@df{r"""^^J%
This file was *autogenerated* from \jobname.tex with sagetex.sty^^J%
version \ST@ver. It contains the contents of all the^^J%
sageexample environments from \jobname.tex. You should be able to^^J%
doctest this file with "sage -t \jobname_doctest.sage".^^J%
^^J%
It is always safe to delete this file; it is not used in typesetting your^^J%
document.^^J}%
\AtEndDocument{\immediate\write\ST@df{"""}}%
\gdef\ST@diddfsetup{x}}%
{\relax}}
%    \end{macrocode}
% \changes{v2.2.5}{2010/03/25}{Write sageexample environment contents to
% a separate file, formatted for doctesting}
% \end{macro}
%
% \begin{macro}{\ST@wdf}
%   This is the compansion to |\ST@wsf|; it writes to the doctest file,
%   assuming that is has been set up. We ignore the |final| option here
%   since nothing in this file is relevant to typesetting the document.
%    \begin{macrocode}
\newcommand{\ST@wdf}[1]{\immediate\write\ST@df{#1}}
%    \end{macrocode}
% \end{macro}
%
% Now we declare our options, which mostly just set flags that we check
% at the beginning of the document, and when running the |.sage| file.
% \changes{v2.0}{2008/04/04}{Add \texttt{epstopdf} option}
% \changes{v2.0}{2008/12/16}{Add \texttt{final} option}
%
% The |final| option controls whether or not we write the |.sage| file;
% the |imagemagick| and |epstopdf| options both want to write something
% to that same file. So we put off all the actual file stuff until the
% beginning of the document---by that time, we'll have processed the
% |final| option (or not) and can check the |\ST@final| flag to see what
% to do. (We must do this because we can't specify code that runs if an
% option \emph{isn't} defined.)
%
% For |final|, we set a flag for other guys to check, and if there's no
% |.sout| file, we warn the user that something fishy is going on.
%    \begin{macrocode}
\DeclareOption{final}{%
  \newcommand{\ST@final}{x}%
  \IfFileExists{\jobname.sagetex.sout}{}{\AtEndDocument{\PackageWarningNoLine{sagetex}%
  {`final' option provided, but \jobname.sagetex.sout^^Jdoesn't exist! No Sage
    input will appear in your document. Remove the `final'^^Joption and
    rerun LaTeX on your document}}}}
%    \end{macrocode}
% For |imagemagick|, we set two flags: one for \LTX and one for Sage.
% It's important that we set |ST@useimagmagick| \emph{before} the
% beginning of the document, so that the graphics commands can check
% that. We do wait until the beginning of the document to do file
% writing stuff.
%    \begin{macrocode}
\DeclareOption{imagemagick}{%
  \newcommand{\ST@useimagemagick}{x}%
  \AtBeginDocument{%
  \@ifundefined{ST@final}{%
    \ST@wsf{_st_.useimagemagick = True}}{}}}
%    \end{macrocode}
% For |epstopdf|, we just set a flag for Sage.
%    \begin{macrocode}
\DeclareOption{epstopdf}{%
\AtBeginDocument{%
\@ifundefined{ST@final}{%
  \ST@wsf{_st_.useepstopdf = True}}{}}}
%    \end{macrocode}
% By default, we check to see if the .py and .sty file versions match.
% But we let the user disable this.
%    \begin{macrocode}
\newcommand{\ST@versioncheck}{True}
\DeclareOption{noversioncheck}{%
  \renewcommand{\ST@versioncheck}{False}}
\ProcessOptions\relax
%    \end{macrocode}
% The |\relax| is a little incantation suggested by the ``\LaTeXe{} for
% class and package writers'' manual, section 4.7.
%
% Pull in the |.sout| file if it exists, or do nothing if it doesn't. I
% suppose we could do this inside an |AtBeginDocument| but I don't see
% any particular reason to do that. It will work whenever we load it. If
% the |.sout| file isn't found, print the usual \TeX-style message. This
% allows programs
% (\href{http://www.phys.psu.edu/~collins/software/latexmk-jcc/}{\texttt{Latexmk}}, for example)
% that read the |.log| file or terminal output to detect
% the need for another typesetting run to do so. If the ``\texttt{No
%   file foo.sout}'' line doesn't work for some software package, please
% let me know and I can change it to use |PackageInfo| or whatever.
%    \begin{macrocode}
\InputIfFileExists{\jobname.sagetex.sout}{}
{\typeout{No file \jobname.sagetex.sout.}}
%    \end{macrocode}
% \changes{v2.1.1}{2009/05/14}{Add typeout if .sout file not found}
%
% The user might load the |hyperref| package after this one (indeed, the
% |hyperref| documentation insists that it be loaded last) or not at
% all---so when we hit the beginning of the document, provide a dummy
% |NoHyper| environment if one hasn't been defined by the |hyperref|
% package. We need this for the |\sage| macro below.
%    \begin{macrocode}
\AtBeginDocument{\provideenvironment{NoHyper}{}{}}
%    \end{macrocode}
%
% \subsubsection{The \texttt{\protect\bslash sage} and
% \texttt{\protect\bslash sagestr} macros}
% \label{sec:sagemacro}
%
% \begin{macro}{\ST@sage}
% \changes{v2.1.1}{2009/05/14}{Add ST@sage, sagestr, and refactor.}
% This macro combines |\ref|, |\label|, and Sage all at once. First, we
% use Sage to get a \LTX representation of whatever you give this
% function. The Sage script writes a |\newlabel| line into the |.sout|
% file, and we read the output using the |\ref| command. Usually, |\ref|
% pulls in a section or theorem number, but it will pull in arbitrary
% text just as well.
%
% The first thing it does it write its argument into the |.sage| file,
% along with a counter so we can produce a unique label. We wrap a
% try/except around the function call so that we can provide a more
% helpful error message in case something goes wrong. (In particular, we
% can tell the user which line of the |.tex| file contains the offending
% code.) Note the difference between |^^J| and |^^J%|: the newline
% immediately after the former puts a space into the output, and the
% percent sign in the latter supresses this.
%    \begin{macrocode}
\newcommand{\ST@sage}[1]{\ST@wsf{%
try:^^J
 _st_.current_tex_line = \the\inputlineno^^J
 _st_.inline(\theST@inline, #1)^^J%
except:^^J
 _st_.goboom(\the\inputlineno)}%
%    \end{macrocode}
% The |inline| function of the Python module is documented on page
% \pageref{inlinefn}. Back in \LTX-land: if paused, say so.
%    \begin{macrocode}
\ifST@paused
  \mbox{(Sage\TeX{} is paused)}%
%    \end{macrocode}
% Otherwise\ldots our use of |\newlabel| and |\ref| seems awfully clever
% until you load the |hyperref| package, which gleefully tries to
% hyperlink the hell out of everything. This is great until it hits one
% of our special |\newlabel|s and gets deeply confused. Fortunately the
% |hyperref| folks are willing to accomodate people like us, and give us
% a |NoHyper| environment.
%    \begin{macrocode}
\else
  \begin{NoHyper}\ref{@sageinline\theST@inline}\end{NoHyper}%
%    \end{macrocode}
% Now check if the label has already been defined. (The internal
% implementation of labels in \LTX involves defining a macro called
% ``|r@@labelname|''.) If it hasn't, we set a flag so that we can tell
% the user to run Sage on the |.sage| file at the end of the run.
%    \begin{macrocode}
  \@ifundefined{r@@sageinline\theST@inline}{\gdef\ST@rerun{x}}{}%
\fi
%    \end{macrocode}
% In any case, the last thing to do is step the counter.
%    \begin{macrocode}
\stepcounter{ST@inline}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sage}
% This is the user-visible macro; it runs Sage's |latex()| on its
% argument.
%    \begin{macrocode}
\newcommand{\sage}[1]{\ST@sage{latex(#1)}}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\sagestr}
% Like above, but doesn't run |latex()| on its argument.
%    \begin{macrocode}
\newcommand{\sagestr}[1]{\ST@sage{#1}}
%    \end{macrocode}
%
% \end{macro}
%
% \begin{macro}{\percent}
% A macro that inserts a percent sign. This is more-or-less stolen from the
% \textsf{Docstrip} manual; there they change the catcode inside a group
% and use |gdef|, but here we try to be more \LaTeX y and use
% |\newcommand|.
%    \begin{macrocode}
\catcode`\%=12
\newcommand{\percent}{%}
\catcode`\%=14
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{The \texttt{\protect\bslash sageplot} macro and friends}
% \label{sec:sageplotmacro}
%
% Plotting is rather more complicated, and requires several helper
% macros that accompany |\sageplot|.
%
% \begin{macro}{\ST@plotdir}
% A little abbreviation for the plot directory. We don't use
% |\graphicspath| because it's
% \href{http://www.tex.ac.uk/cgi-bin/texfaq2html?label=graphicspath}{
% apparently slow}---also, since we know right where our plots are
% going, no need to have \LTX looking for them.
%    \begin{macrocode}
\newcommand{\ST@plotdir}{sage-plots-for-\jobname.tex}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\ST@missingfilebox}
% The code that makes the ``file not found'' box. This shows up in a
% couple places below, so let's just define it once.
%    \begin{macrocode}
\newcommand{\ST@missingfilebox}{\framebox[2cm]{\rule[-1cm]{0cm}{2cm}\textbf{??}}}
%    \end{macrocode}
% \end{macro}
% \begin{macro}{\sageplot}
% \changes{v1.3}{2008/03/08}{Iron out warnings, cool \TikZ flowchart}
% This function is similar to |\sage|. The neat thing that we take
% advantage of is that commas aren't special for arguments to \LTX
% commands, so it's easy to capture a bunch of keyword arguments that
% get passed right into a Python function.
%
% This macro has two optional arguments, which can't be defined using
% \LTX's |\newcommand|; we use Scott Pakin's brilliant
% \href{http://tug.ctan.org/tex-archive/support/newcommand/}{|newcommand|}
% package to create this macro; the options I fed to his script were
% similar to this:
%\begin{center}
% |MACRO sageplot OPT[#1={width}] OPT[#2={notprovided}] #3|
%\end{center}
% Observe that we are using a Python script to write \LTX code which
% writes Python code which writes \LTX code. Crazy!
%
% Here's the wrapper command which does whatever magic we need to get
% two optional arguments.
%    \begin{macrocode}
\newcommand{\sageplot}[1][]{%
  \@ifnextchar[{\ST@sageplot[#1]}{\ST@sageplot[#1][notprovided]}}
%    \end{macrocode}
% \changes{v2.3.2}{2011/06/17}{Remove ``.75 textwidth'' default option}
% The first optional argument |#1| will get shoved right into the
% optional argument for |\includegraphics|, so the user has easy control
% over the \LTX aspects of the plotting. (Perhaps a future version
% of \ST will allow the user to specify in the package options a set of
% default options to be used throughout.) The second optional argument
% |#2| is the file format and allows us to tell what files to look for.
% It defaults to ``notprovided'', which tells the Python module to
% create EPS and PDF files. Everything in |#3| gets put into the Python
% function call, so the user can put in keyword arguments there which
% get interpreted correctly by Python.
%
% \begin{macro}{\ST@sageplot}
% \changes{v2.0}{2008/12/16}{Change to use only keyword arguments: see issue
% 2 on bitbucket tracker}
% Let's see the real code here. We write a couple lines to the |.sage|
% file, including a counter, input line number, and all of the mandatory
% argument; all this is wrapped in another try/except.
%    \begin{macrocode}
\def\ST@sageplot[#1][#2]#3{\ST@wsf{try:^^J
 _st_.current_tex_line = \the\inputlineno^^J
 _st_.plot(\theST@plot, format='#2', _p_=#3)^^Jexcept:^^J
 _st_.goboom(\the\inputlineno)}%
%    \end{macrocode}
% The Python |plot| function is documented on page~\pageref{plotfn}.
%
% Now we include the appropriate graphics file. Because the user might
% be producing DVI or PDF files, and have supplied a file format or not,
% and so on, the logic we follow is a bit complicated.
% \autoref{f:sageplottree} shows what we do; for completeness---and
% because I think drawing trees with \TikZ is really cool---we show what
% |\ST@inclgrfx| does in \autoref{f:stig}. This entire complicated
% business is intended to avoid doing an |\includegraphics| command on a
% file that doesn't exist, and to issue warnings appropriate to the
% situation.
%
% \begin{figure}
%   \centering
%   \begin{tikzpicture}
%     \tikzstyle{level 1}=[sibling distance=6cm]
%     \tikzstyle{level 2}=[sibling distance=3cm]
%     \node [box] {DVI or PDF?}
%       child {node [box] {Format provided?}
%         child {node [box] {STig EPS}
%           edge from parent node[left] {no}}
%         child {node [box] {IM option set?}
%           child {node [box, text width=3cm] {Warn that DVI + PNG = bad}
%             edge from parent node[left] {no}}
%           child {node [box] {STig EPS}
%             edge from parent node[right] {yes}}
%           edge from parent node[right] {yes}}
%         edge from parent node[left] {DVI}}
%       child {node [box] {Format provided?}
%         child {node [box] {STig PDF}
%           edge from parent node[left] {no}}
%         child {node [box] {STig \texttt{\#2}}
%           edge from parent node[right] {yes}}
%         edge from parent node[right] {PDF}};
%   \end{tikzpicture}
%   \caption{The logic tree that \texttt{\bslash sageplot} uses to
%   decide whether to run \texttt{\bslash includegraphics} or to yell at
%   the user. ``Format'' is the \texttt{\#2} argument to \texttt{\bslash
%   sageplot}, ``STig ext''
%   means a call to \texttt{\bslash ST@inclgrfx} with ``ext'' as the
%   second argument, and ``IM'' is Imagemagick.}
%   \label{f:sageplottree}
% \end{figure}
%
% If we are creating a PDF, we check to see if the user asked for a
% different format, and use that if necessary:
%    \begin{macrocode}
\ifthenelse{\boolean{pdf} \or \boolean{xetex}}{
  \ifthenelse{\equal{#2}{notprovided}}%
    {\ST@inclgrfx{#1}{pdf}}%
    {\ST@inclgrfx{#1}{#2}}}
%    \end{macrocode}
% Otherwise, we are creating a DVI file, which only supports EPS. If the
% user provided a format anyway, don't include the file (since it won't
% work) and warn the user about this. (Unless the file doesn't exist, in
% which case we do the same thing that |\ST@inclgrfx| does.)
%    \begin{macrocode}
{ \ifthenelse{\equal{#2}{notprovided}}%
    {\ST@inclgrfx{#1}{eps}}%
%    \end{macrocode}
% If a format is provided, we check to see if we're using the
% imagemagick option. If not, we're going to issue some sort of warning,
% depending on whether the file exists yet or not.
%    \begin{macrocode}
    {\@ifundefined{ST@useimagemagick}%
      {\IfFileExists{\ST@plotdir/plot-\theST@plot.#2}%
        {\ST@missingfilebox%
         \PackageWarning{sagetex}{Graphics file
         \ST@plotdir/plot-\theST@plot.#2\space on page \thepage\space
         cannot be used with DVI output. Use pdflatex or create an EPS
         file. Plot command is}}%
        {\ST@missingfilebox%
         \PackageWarning{sagetex}{Graphics file
         \ST@plotdir/plot-\theST@plot.#2\space on page \thepage\space
         does not exist. Plot command is}%
         \gdef\ST@rerun{x}}}%
%    \end{macrocode}
% Otherwise, we are using Imagemagick, so try to include an EPS file
% anyway.
%    \begin{macrocode}
    {\ST@inclgrfx{#1}{eps}}}}
%    \end{macrocode}
% Step the counter and we're done with the usual work.
%    \begin{macrocode}
\stepcounter{ST@plot}}
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{\ST@inclgrfx}
% This command includes the requested graphics file (|#2| is the
% extension) with the requested options (|#1|) if the file exists. Note
% that it just needs to know the extension, since we use a counter for
% the filename. If we are paused, it just puts in a little box saying
% so.
%    \begin{macrocode}
\newcommand{\ST@inclgrfx}[2]{\ifST@paused
  \fbox{\rule[-1cm]{0cm}{2cm}Sage\TeX{} is paused; no graphic}
\else
  \IfFileExists{\ST@plotdir/plot-\theST@plot.#2}%
    {\includegraphics[#1]{\ST@plotdir/plot-\theST@plot.#2}}%
%    \end{macrocode}
% If the file doesn't exist, we try one more thing before giving up: the
% Python module will automatically fall back to saving as a PNG file if
% saving as an EPS or PDF file fails. So if making a PDF, we look for a
% PNG file.
%
% If the file isn't there, we insert a little box to indicate it wasn't
% found, issue a warning that we didn't find a graphics file, then set a
% flag that, at the end of the run, tells the user to run Sage again.
%    \begin{macrocode}
    {\IfFileExists{\ST@plotdir/plot-\theST@plot.png}%
       {\ifpdf
           \ST@inclgrfx{#1}{png}
         \else
           \PackageWarning{sagetex}{Graphics file
           \ST@plotdir/plot-\theST@plot.png on page \thepage\space not
            supported; try using pdflatex. Plot command is}%
        \fi}%
       {\ST@missingfilebox%
       \PackageWarning{sagetex}{Graphics file
       \ST@plotdir/plot-\theST@plot.#2\space on page \thepage\space does not
       exist. Plot command is}%
       \gdef\ST@rerun{x}}}
\fi}
%    \end{macrocode}
% \autoref{f:stig} makes this a bit clearer.
% \begin{figure}
%   \centering
%   \begin{tikzpicture}
%     \tikzstyle{level 1}=[sibling distance=4cm]
%     \node [box] {Paused?}
%       child {node [box] {Insert ``we're paused'' box}
%         edge from parent node[left] {yes}}
%       child {node [box] {Does EXT file exist?}
%         child {node [box] {Does a PNG file exist?}
%           child {node [box] {Making a PDF?}
%             child {node [box] {\texttt{includegraphics} PNG}
%               edge from parent node[left] {yes}}
%             child {node [box, text width=2cm] {Warning: DVI, PNG incompatible}
%               edge from parent node[left] {no}}
%             edge from parent node[left] {yes}}
%           child {node [box, text width = 2.125cm] {Warn user to rerun Sage}
%             edge from parent node[left] {no}}
%           edge from parent node[left] {no}}
%         child {node [box] {Use \texttt{includegraphics}}
%           edge from parent node[right] {yes}}
%         edge from parent node[right] {no}};
%   \end{tikzpicture}
%   \caption{The logic used by the \texttt{\bslash ST@inclgrfx}
%   command.}
%   \label{f:stig}
% \end{figure}
% \end{macro}
%
% \subsubsection{Verbatim-like environments}
% \label{sec:verbatim-envs}
%
% \begin{macro}{\ST@beginsfbl}
% This is ``begin |.sage| file block'', an internal-use abbreviation
% that sets things up when we start writing a chunk of Sage code to
% the |.sage| file. It begins with some \TeX{} magic that fixes
% spacing, then puts the start of a try/except block in the |.sage|
% file---this not only allows the user to indent code without
% Sage/Python complaining about indentation, but lets us tell the user
% where things went wrong. The |blockbegin| and |blockend| functions
% are documented on page~\pageref{blocksbeginend}. The last bit is some
% magic from the |verbatim| package manual that makes \LTX respect
% line breaks.
%    \begin{macrocode}
\newcommand{\ST@beginsfbl}{%
  \@bsphack\ST@wsf{%
_st_.current_tex_line = \the\inputlineno^^J%
_st_.blockbegin()^^Jtry:}%
  \let\do\@makeother\dospecials\catcode`\^^M\active}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{\ST@endsfbl}
% The companion to |\ST@beginsfbl|.
%    \begin{macrocode}
\newcommand{\ST@endsfbl}{%
\ST@wsf{except:^^J
 _st_.goboom(\the\inputlineno)^^J_st_.blockend()}}
%    \end{macrocode}
% \end{macro}
%
% Now let's define the ``verbatim-like'' environments. There are four
% possibilities, corresponding to the two independent choices of
% typesetting the code or not, and writing to the |.sage| file or not.
%
% \begin{environment}{sageblock}
% This environment does both: it typesets your code and puts it into the
% |.sage| file for execution by Sage.
%    \begin{macrocode}
\newenvironment{sageblock}{\ST@beginsfbl%
%    \end{macrocode}
% The space between |\ST@wsf{| and |\the| is crucial! It, along with the
% ``|try:|'', is what allows the user to indent code if they like. This
% line sends stuff to the |.sage| file.
%    \begin{macrocode}
\def\verbatim@processline{\ST@wsf{ \the\verbatim@line}%
%    \end{macrocode}
% Next, we typeset your code and start the verbatim environment.
%    \begin{macrocode}
\hspace{\sagetexindent}\the\verbatim@line\par}%
\verbatim}%
%    \end{macrocode}
% At the end of the environment, we put a chunk into the |.sage| file
% and stop the verbatim environment.
%    \begin{macrocode}
{\ST@endsfbl\endverbatim}
%    \end{macrocode}
% \end{environment}
%
% \begin{environment}{sagesilent}
% This is from the |verbatim| package manual. It's just like the above,
% except we don't typeset anything.
%    \begin{macrocode}
\newenvironment{sagesilent}{\ST@beginsfbl%
\def\verbatim@processline{\ST@wsf{ \the\verbatim@line}}%
\verbatim@start}%
{\ST@endsfbl\@esphack}
%    \end{macrocode}
% \end{environment}
%
% \begin{environment}{sageverbatim}
% The opposite of |sagesilent|. This is exactly the same as the verbatim
% environment, except that we include some indentation to be consistent
% with other typeset Sage code.
%    \begin{macrocode}
\newenvironment{sageverbatim}{%
\def\verbatim@processline{\hspace{\sagetexindent}\the\verbatim@line\par}%
\verbatim}%
{\endverbatim}
%    \end{macrocode}
% \end{environment}
%
% Logically, we now need an environment which neither typesets
% \emph{nor} writes code to the |.sage| file. The verbatim package's
% |comment| environment does that.\\
%
% \begin{environment}{sageexample}
%   Finally, we have an environment which is mostly-but-not-entirely
%   verbatim; this is the example environment, which takes input like
%   Sage doctests, and prints out the commands verbatim but nicely
%   typesets the output of those commands. This and the corresponding
%   Python function are originally due to Nicolas M. Thi\'ery.
%    \begin{macrocode}
\newcommand{\sageexampleincludetextoutput}{False}
\newenvironment{sageexample}{%
   \ST@wsf{%
try:^^J
 _st_.current_tex_line = \the\inputlineno^^J
 _st_.doctest(\theST@inline, r"""}%
   \ST@dodfsetup%
   \ST@wdf{Sage example, line \the\inputlineno::^^J}%
   \begingroup%
   \@bsphack%
   \let\do\@makeother\dospecials%
   \catcode`\^^M\active%
   \def\verbatim@processline{%
     \ST@wsf{\the\verbatim@line}%
     \ST@wdf{\the\verbatim@line}%
   }%
   \verbatim@start%
}
{
  \@esphack%
  \endgroup%
  \ST@wsf{%
    """, globals(), locals(), \sageexampleincludetextoutput)^^Jexcept:^^J
    _st_.goboom(\the\inputlineno)}%
  \ifST@paused%
    \mbox{(Sage\TeX{} is paused)}%
  \else%
    \begin{NoHyper}\ref{@sageinline\theST@inline}\end{NoHyper}%
    \@ifundefined{r@@sageinline\theST@inline}{\gdef\ST@rerun{x}}{}%
  \fi%
  \ST@wdf{}%
  \stepcounter{ST@inline}}
%    \end{macrocode}
% \changes{v2.2.4}{2010/03/14}{Add first support for
%   \texttt{sageexample} environment}
% \end{environment}
%
%
% \begin{environment}{sagecommandline}
% This environment is similar to the |sageexample| environment, but
% typesets the Sage output as text with Python syntax highlighting.
%    \begin{macrocode}
\newcommand{\sagecommandlinetextoutput}{True}
\newlength{\sagecommandlineskip}
\setlength{\sagecommandlineskip}{8pt}
\newenvironment{sagecommandline}{%
   \ST@wsf{%
try:^^J
 _st_.current_tex_line = \the\inputlineno^^J
 _st_.commandline(\theST@cmdline, r"""}%
   \ST@dodfsetup%
   \ST@wdf{Sage commandline, line \the\inputlineno::^^J}%
   \begingroup%
   \@bsphack%
   \let\do\@makeother\dospecials%
   \catcode`\^^M\active%
   \def\verbatim@processline{%
     \ST@wsf{\the\verbatim@line}%
     \ST@wdf{\the\verbatim@line}%
   }%
   \verbatim@start%
}
{
  \@esphack%
  \endgroup%
  \ST@wsf{%
    """, globals(), locals(), \sagecommandlinetextoutput)^^Jexcept:^^J
    _st_.goboom(\the\inputlineno)}%
  \ifST@paused%
    \mbox{(Sage\TeX{} is paused)}%
  \else%
    \begin{NoHyper}\ref{@sagecmdline\theST@cmdline}\end{NoHyper}%
    \@ifundefined{r@@sagecmdline\theST@cmdline}{\gdef\ST@rerun{x}}{}%
  \fi%
  \ST@wdf{}%
  \stepcounter{ST@cmdline}}
%    \end{macrocode}
% \end{environment}
%
% \subsubsection{Pausing \ST}
% \label{sec:pausing-sagetex}
%
% How can one have Sage to stop processing \ST output for a little
% while, and then start again? At first I thought I would need some sort
% of ``goto'' statement in Python, but later realized that there's a
% dead simple solution: write triple quotes to the |.sage| file to
% comment out the code. Okay, so this isn't \emph{really} commenting out
% the code; PEP 8 says block comments should use ``|#|'' and Sage will
% read in the ``commented-out'' code as a string literal. For the
% purposes of \ST, I think this is a good decision, though, since (1)
% the pausing mechanism is orthogonal to everything else, which makes it
% easier to not screw up other code, and (2) it will always work.
%
% This illustrates what I really like about \ST: it mixes \LTX and
% Sage/Python, and often what is difficult or impossible in one system
% is trivial in the other.
%
% \begin{macro}{sagetexpause}
% This macro pauses \ST by effectively commenting out code in the
% |.sage| file. When running the corresponding |.sage| file, Sage will
% skip over any commands issued while \ST is paused.
%    \begin{macrocode}
\newcommand{\sagetexpause}{\ifST@paused\relax\else
\ST@wsf{print('SageTeX paused on \jobname.tex line \the\inputlineno')^^J"""}
\ST@pausedtrue
\fi}
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{sagetexunpause}
% This is the obvious companion to |\sagetexpause|.
%    \begin{macrocode}
\newcommand{\sagetexunpause}{\ifST@paused
\ST@wsf{"""^^Jprint('SageTeX unpaused on \jobname.tex line \the\inputlineno')}
\ST@pausedfalse
\fi}
%    \end{macrocode}
% \end{macro}
%
% \subsubsection{End-of-document cleanup}
% \label{sec:end-of-doc-cleanup}
%
% We tell the Sage script to write some information to the |.sout| file,
% then check to see if |ST@rerun| ever got defined. If not, all the
% inline formulas and plots worked, so do nothing. We check to see if
% we're paused first, so that we can finish the triple-quoted string in
% the |.sage| file.
%    \begin{macrocode}
\AtEndDocument{\ifST@paused
\ST@wsf{"""^^Jprint('SageTeX unpaused at end of \jobname.tex')}
\fi
\ST@wsf{_st_.endofdoc()}%
\@ifundefined{ST@rerun}{}%
%    \end{macrocode}
% Otherwise, we issue a warning to tell the user to run Sage on the
% |.sage| file. Part of the reason we do this is that, by using |\ref|
% to pull in the inlines, \LTX will complain about undefined references
% if you haven't run the Sage script---and for many \LTX users, myself
% included, the warning ``there were undefined references'' is a signal
% to run \LTX again. But to fix these particular undefined references,
% you need to run \emph{Sage}. We also suppress file-not-found errors
% for graphics files, and need to tell the user what to do about that.
%
% At any rate, we tell the user to run Sage if it's necessary.
%    \begin{macrocode}
{\typeout{*********************************************************************}
\PackageWarningNoLine{sagetex}{there were undefined Sage formulas and/or
plots.^^JRun Sage on \jobname.sagetex.sage, and then run LaTeX on \jobname.tex
again}}
\typeout{*********************************************************************}}
%    \end{macrocode}
%
%
% \subsection{The Python module}
% \label{sec:py-file}
%
% \iffalse
% Hey, docstrip! Stop putting code into the .sty file, and start
% putting it into the .py file.
%</latex>
%<*python>
% Thanks.
% \fi
%
% The style file writes things to the |.sage| file and reads them from
% the |.sout| file. The Python module provides functions that help
% produce the |.sout| file from the |.sage| file.
%
% \paragraph{A note on Python and \textsf{Docstrip}} There is one tiny
% potential source of confusion when documenting Python code with
% \textsf{Docstrip}: the percent sign. If you have a long line of Python
% code which includes a percent sign for string formatting and you break
% the line with a backslash and begin the next line with a percent sign,
% that line \emph{will not} be written to the output file. This is only
% a problem if you \emph{begin} the line with a (single) percent sign;
% there are no troubles otherwise.\\
%
% On to the code. Munge the version string (which we get from
% \texttt{sagetex.dtx}) to extract what we want, then import what we
% need:
%    \begin{macrocode}
pyversion = ' '.join(__version__.strip('[').split()[0:2])
from sage.misc.latex import latex
from sage.repl.preparse import preparse
from six import PY3
import sys
import os
import os.path
import hashlib
import traceback
import subprocess
import shutil
import re
from collections import defaultdict
%    \end{macrocode}
% Define an exception class for version mismatches. I suppose I could
% just use |ValueError|, but this is easy enough:
%    \begin{macrocode}
class VersionError(Exception):
    pass
%    \end{macrocode}
% Sometimes our macros that write things to the |.sout| file get
% evaluated twice, most commonly in the ``fancy'' AMS environments such
% as |align| and |multline|. So we need to keep track of the counters
% we've seen so we don't write labels to the |.sout| file more than
% once. We have more than one kind of label, so a dictionary is the
% natural way to store the counters we've seen for each kind of label.
% For convenience let's make a dictionary subclass for which (1) values
% default to $-1$, and (2) there's an |increment(key)| function that just
% increments the value corresponding to the key.
%    \begin{macrocode}
class MyDict(defaultdict):
    def __init__(self, *args, **kwargs):
        defaultdict.__init__(self, *args, **kwargs)
        self.default_factory = lambda: -1

    def increment(self, key):
        self[key] = self[key] + 1
%    \end{macrocode}
% Here's a helper function used by |doctest|; it works ike |j.join(xs)|,
% but ensures exactly one copy of |j| between the strings in |xs|.
% Intended for |j| to be a single character, particularly newline so
% that you can join things with no extra blank lines.
%    \begin{macrocode}
def joinone(j, xs_):
    if len(xs_) >= 2:
        xs = ([xs_[0].rstrip(j)] +
              [x.strip(j) for x in xs_[1:-1]] +
              [xs_[-1].lstrip(j)])
    else:
        xs = xs_
    return j.join(xs)
%    \end{macrocode}
% Another helper, used by |commandline| (and maybe, someday,
% |doctest|?). In each line, we look for a possibly empty sequence of
% spaces followed by a non-whitespace character, so we can distinguish
% between whitespace-only lines (which we ignore) and lines that have no
% leading spaces.
%
% One tiny possible problem: you might have a line of only, say, two
% spaces, but perhaps the ``real'' lines all start with at least three
% spaces. Then you would, for that line, do |line[2:]|. That seems like
% it might raise an error, since the line only has indices 0 and 1, but
% Python's indexing handles this perfectly: in that case, |line[2:]|
% will be the empty string, which is fine for our purposes.
%    \begin{macrocode}
def strip_common_leading_spaces(s):
    lines = s.splitlines()
    lead = min(m.end() for m in
                  [re.match(' *\S', line) for line in lines]
                  if m is not None) - 1
    return '\n'.join(line[lead:] for line in lines)
%    \end{macrocode}
%
% \subsubsection{The \texttt{SageTeXProcessor} class}
% \label{sec:sagetexprocessorclass}
%
% The star of the show, as it were. We define a |SageTeXProcessor| class
% so that it's a bit easier to carry around internal state. We used to
% just have some global variables and a bunch of functions, but this
% seems a bit nicer and easier.
%    \begin{macrocode}
class SageTeXProcessor():
%    \end{macrocode}
% If the original |.tex| file has spaces in its name, the |\jobname|
% we get is surrounded by double quotes, so fix that. Technically, it
% is possible to have double quotes in a legitimate filename, but
% dealing with that sort of quoting is
% \href{http://tug.org/pipermail/xetex/2006-August/004712.html}{unpleasant}.
% And yes, we're ignoring the possibility of tabs and other whitespace
% in the filename. Patches for handling pathological filenames welcome.
%
% \changes{v2.3.1}{2011/02/02}{Handle filenames with
% spaces in SageTeXProcessor and sagecommandline env.}
% \changes{v2.3.2}{2012/01/13}{Improve version mismatch check. Fixes
% trac ticket 8035.}
%    \begin{macrocode}
  def __init__(self, jobname, version=None, version_check=True):
    if version != pyversion:
      errstr = """versions of .sty and .py files do not match.
{0}.sagetex.sage was generated by sagetex.sty version "{1}", but
is being processed by sagetex.py version "{2}".
Please make sure that TeX is using the sagetex.sty 
from your current version of Sage; see
http://doc.sagemath.org/html/en/tutorial/sagetex.html.""".format(jobname,
  version, pyversion)
      if version_check:
        raise VersionError(errstr)
      else:
        print('**** WARNING! Skipping version check for .sty and .py files, and')
        print(errstr)
    if ' ' in jobname:
      jobname = jobname.strip('"')
    self.progress('Processing Sage code for {0}.tex...'.format(jobname))
    self.didinitplot = False
    self.useimagemagick = False
    self.useepstopdf = False
    self.plotdir = 'sage-plots-for-' + jobname + '.tex'
    self.filename = jobname
    self.name = os.path.splitext(jobname)[0]
    autogenstr = """% This file was *autogenerated* from {0}.sagetex.sage with
 % sagetex.py version {1}\n""".format(self.name, version)
%    \end{macrocode}
% Don't remove the space before the percent sign above!
%
% \LTX environments such as |align| evaluate their arguments twice after
% doing |\savecounters@|, so if you do |\sage| inside such an environment,
% it will result in two labels with the same name in the |.sout| file and
% the user sees a warning when typesetting. So we keep track of the
% largest label we've seen so that we don't write two labels with the same
% name.
%    \begin{macrocode}
    self.max_counter_seen = MyDict()
%    \end{macrocode}
% Open a |.sout.tmp| file and write all our output to that. Then, when
% we're done, we move that to |.sout|. The ``autogenerated'' line is
% basically the same as the lines that get put at the top of preparsed
% Sage files; we are automatically generating a file with Sage, so it
% seems reasonable to add it. Add in the version to help debugging
% version mismatch problems.
%    \begin{macrocode}
    self.souttmp = open(self.filename + '.sagetex.sout.tmp', 'w')
    self.souttmp.write(autogenstr)
%    \end{macrocode}
% In addition to the |.sout| file, the |sagecommandline| also needs a
% |.scmd| file. As before, we use a |.scmd.tmp| file and rename it
% later on. We store the position so that |commandline| can tell the
% |listings| package what lines in the |.scmd| file to pull in.
%    \begin{macrocode}
    self.scmdtmp = open(self.filename + '.sagetex.scmd.tmp', 'w')
    self.scmdtmp.write(autogenstr)
    self.scmdpos = 3
%    \end{macrocode}
%
% \begin{macro}{progress}
% This function just prints stuff. It allows us to not print a
% linebreak, so you can get ``|start...|'' (little time spent
% processing) ``|end|'' on one line.
%    \begin{macrocode}
  def progress(self, t,linebreak=True):
    if linebreak:
      print(t)
    else:
      sys.stdout.write(t)
      sys.stdout.flush()
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{initplot}
% \phantomsection\label{initplot}
% We only want to create the plots directory if the user actually plots
% something. This function creates the directory and sets the
% |didinitplot| flag after doing so. We make a directory based on the
% \LTX file being processed so that if there are multiple |.tex| files
% in a directory, we don't overwrite plots from another file.
%    \begin{macrocode}
  def initplot(self):
    self.progress('Initializing plots directory')
%    \end{macrocode}
% We hard-code the |.tex| extension, which is fine in the overwhelming
% majority of cases, although it does cause minor confusion when
% building the documentation. If it turns out lots of people use, say, a
% |ltx| extension or whatever, We could find out the correct extension,
% but it would involve a lot of irritating mucking around---on
% |comp.text.tex|, the best solution I found for finding the file
% extension is to look through the |.log| file. (Although see the
% \texttt{currfile} package.)
%    \begin{macrocode}
    if os.path.isdir(self.plotdir):
      shutil.rmtree(self.plotdir)
    os.mkdir(self.plotdir)
    self.didinitplot = True
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{inline}
% \phantomsection\label{inlinefn}
% This function works with |\sage| from the style file (see
% \autoref{sec:sagemacro}) to put Sage output into your \LTX file.
% Usually, when you use |\label|, it writes a line such as
% \begin{center}
%   |\newlabel{labelname}{{section number}{page number}}|
% \end{center}
% to the |.aux| file. When you use the |hyperref| package, there are
% more fields in the second argument, but the first two fields are the
% same. The |\ref| command just pulls in what's in the first field of
% the second argument, so we can hijack this mechanism for our own
% nefarious purposes. The function writes a |\newlabel| line with a
% label made from a counter and the text from running Sage on |s|.
%
% When the user does |\sage| inside certain displayed math environments
% (|align| is the most common culprit) this function will get called
% twice with exactly the same arguments. We check to see what labels
% we've seen and immediately bail if we've written this label before.
%
% The |labelname| defaults to the the name used by the usual |\sage|
% inline macro, but this function is also used by the |sagecommandline|
% environment. It's important to keep the corresponding labels separate,
% because |\sage| macros often (for example) appear inside math mode,
% and the labels from |sagecommandline| contain a |lstlistings|
% environment---pulling such an environment into math mode produces
% strange, unrecoverable errors, and if you can't typeset your file, you
% can't produce an updated |.sagetex.sage| file to run Sage on to
% produce a reasonable |.sagetext.sout| file that will fix the label
% problem. So it works much better to use distinct labels for such
% things.
% \changes{v2.3.3}{2012/01/16}{check label name when comparing against
% maximum counter seen; trac ticket 12267}
%
% We print out the line number so if something goes wrong, the user can
% more easily track down the offending |\sage| command in the source
% file.
%
% That's a lot of explanation for a short function:
%    \begin{macrocode}
  def inline(self, counter, s, labelname='sageinline'):
      if counter <= self.max_counter_seen[labelname]:
          return
      else:
          self.max_counter_seen.increment(labelname)
      if labelname == 'sageinline':
          self.progress('Inline formula {0} (line {1})'.format(counter, self.current_tex_line))
      elif labelname == 'sagecmdline':
          pass # output message already printed
      else:
          raise ValueError('inline() got a bad labelname "{0}"'.format(labelname))
      self.souttmp.write(r'\newlabel{@' + labelname + str(counter) + 
                         '}{{%\n' + s.rstrip() + '}{}{}{}{}}\n')
%    \end{macrocode}
% We are using five fields, just like |hyperref| does, because that
% works whether or not |hyperref| is loaded. Using two fields, as in
% plain \LTX, doesn't work if |hyperref| is loaded.
% \end{macro}
%
% \begin{macro}{savecmd}
%   Analogous to |inline|, this method saves the input string |s| to the
%   |souttmp| file. It returns the first and last line of the
%   newly-added output so that |commandline| can tell the |listings|
%   package where to get stuff.
%    \begin{macrocode}
  def savecmd(self, s):
      self.scmdtmp.write(s.rstrip() + "\n")
      begin = self.scmdpos
      end = begin + len(s.splitlines()) - 1
      self.scmdpos = end + 1
      return begin, end
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{blockbegin}
% \begin{macro}{blockend}
% \phantomsection\label{blocksbeginend}
% This function and its companion used to write stuff to the |.sout|
% file, but now they just update the user on our progress evaluating a
% code block. The verbatim-like environments of
% \autoref{sec:verbatim-envs} use these functions.
%    \begin{macrocode}
  def blockbegin(self):
    self.progress('Code block (line {}) begin...'.format(self.current_tex_line), False)
  def blockend(self):
    self.progress('end')
%    \end{macrocode}
% \end{macro}
% \end{macro}
%
% \begin{macro}{splitsagecmds}
%   Given a string |s| of doctest-like Sage code, this function returns
%   a list of tuples |(i, j, cmd)|, where |cmd| is a string representing
%   a Sage command, with the initial prompt and continuation lines
%   stripped, |i| is the position in |s| where |cmd| starts, and |j| is
%   the starting position in |s| of the purported output from the
%   command that was included in |s|.
%
%   This is used by |doctest| and |commandline|, below.
%
%   For example, this turns the string
%   \begin{quote}
%   |'''|\\
%   |    sage: 1+1|\\
%   |    2|\\
%   |    sage: y = 1729|\\
%   |    sage: 10^3 + 9^3 == 12^3 + 1^3 == y|\\
%   |    sage: gcd(9999999,|\\
%   |    ....: 123456)|\\
%   |    3|\\
%   |    sage: factor(x^2 + 2*x + 1)|\\
%   |    (x + 1)^2|\\
%   |'''|
%   \end{quote}
%   into
%   \begin{quote}
%   |[(0, 18, '1+1'),|\\
%   | (28, 51, 'y = 1729'),|\\
%   | (51, 95, '10^3 + 9^3 == 12^3 + 1^3 == y'),|\\
%   | (95, 144, 'gcd(9999999,\n123456)'),|\\
%   | (154, 190, 'factor(x^2 + 2*x + 1)')]|
%   \end{quote}
%   You can reconstruct the sequence of commands and their output with
%   something like
%   \begin{quote}
%   |splitup = split_sage_cmds(s)|\\
%   |oldout = splitup[0][1]|\\
%   |print('=' * 50)|\\
%   |print('==== Command:')|\\
%   |print(s[splitup[0][0]:oldout])|\\
%   |for start, out, _ in splitup[1:]:|\\
%   |    print('==== Given output:')|\\
%   |    print(s[oldout:start])|\\
%   |    print('=' * 50)|\\
%   |    print('==== Command:')|\\
%   |    print(s[start:out])|\\
%   |    oldout = out|\\
%   |print('==== Given output:')|\\
%   |print(s[oldout:])|
%   \end{quote}
%    \begin{macrocode}
  def split_sage_cmds(self, s):
      prompt = '\n' + r'\s*sage: '
      oldcont = r'\s*\.\.\.'
      cont = r'\s*\.\.\.\.: '
%    \end{macrocode}
% Prepending a newline to |s| ensures that the list from |re.split()|
% begins with something we can ignore---and so that the |re.split()|
% returns $n+1$ groups for $n$ matches, so therefore |split| and
% |starts| match up.
%    \begin{macrocode}
      split = re.split(prompt, '\n' + s)[1:]
      starts = [m.start() - 1 for m in re.finditer(prompt, '\n' + s)]
%    \end{macrocode}
% The prepended newline messes up the first element of |starts|, fix
% that:
%    \begin{macrocode}
      starts[0] = re.search(prompt, s).start()
%    \end{macrocode}
% Now find where the outputs start. We need this because |doctest()| may
% or may not print the outputs. The idea is: for each |start|ing
% position, advance over the prompt that we know is there, then look for
% the rightmost continuation marker between the current prompt and the
% next one, and \emph{then} look for the newline following that. That
% position is where the output begins.
%    \begin{macrocode}
      outputs = []
      for i, j in zip(starts, starts[1:] + [len(s)]):
          k = i + re.match(prompt, s[i:j]).end()
          try:
              k += [m.end() for m in re.finditer(cont, s[k:j])][-1]
          except IndexError:
              pass
          end = s.find('\n', k)
          outputs.append(end)
%    \end{macrocode}
% Now we take each command group, split it up, and look for all the
% continuation lines. We append those, stripping off the continuation
% marks. We also do some error checking so that users with documents
% that use the old |...| continuation marks get a reasonable error
% message.
%    \begin{macrocode}
      ret = []
      for start, end, g in zip(starts, outputs, split):
          lines = g.splitlines()
          cmd = lines[:1]
          for line in lines[1:]:
              has_old_cont = re.match(oldcont, line)
              has_cont = re.match(cont, line)
              if has_old_cont and not has_cont:
                  raise SyntaxError(""" SageTeX no longer supports "..." for line continuation in sagexample and
sagecommandline environments. Use "....:", which matches what the Sage
interpreter uses. See the documentation and example file in
SAGE_ROOT/venv/share/doc/sagetex.""")
              if has_cont:
                  cmd.append(line[has_cont.end():])
          ret.append((start, end, '\n'.join(cmd)))
      return ret
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{doctest}
%   This function handles the |sageexample| environment, which typesets
%   Sage code and its output. We call it |doctest| because the format is
%   just like that for doctests in the Sage library.
%
%  The idea is:
% \begin{enumerate}
% \item Get the literal text for each command, wrap that in
%   |SaveVerbatim|, write that (possibly with its associated output from
%   the |.tex| file) to the |sout| file.
% \item Accumulate a corresponding |UseVerbatim| and typeset output so
%   that we can call |inline()| at the end and pull in all this stuff.
% \item For the output: try to |eval()| the processed command (the one
%   with the prompts and continuation marks stripped). If that succeeds,
%   we run |latex()| on it and display that below the verbatim text from
%   above. If that fails, it's because you have a statement and not an
%   expression---there's no output from such a thing (well, none that we
%   can capture, anyway) so no need to typeset output.
% \end{enumerate}
%    \begin{macrocode}
  def doctest(self, counter, s, globals, locals, include_text_output):
      self.progress('Sage example {0} (line {1})'.format(counter, self.current_tex_line))
      splitup = self.split_sage_cmds(s)
      tex_strs = []
      for i in range(len(splitup)):
          boxname = '@sageinline{}-code{}'.format(counter, i)
          to_tmp = [r'\begin{SaveVerbatim}{' + boxname + '}',
                    s[splitup[i][0]:splitup[i][1]]]
          if include_text_output:
              try:
                  to_tmp.append(s[splitup[i][1]:splitup[i+1][0]])
              except IndexError:
                  to_tmp.append(s[splitup[i][1]:])
          to_tmp.append('\\end{SaveVerbatim}\n')
          self.souttmp.write(joinone('\n', to_tmp))
%    \end{macrocode}
% Now we build up something that we can send to |inline()|, which will
% pull it into the document using its usual label mechanism.
%
% The verbatim stuff seems to end with a bit of vertical space, so don't
% start the displaymath environment with unnecessary vertical
% space---the displayskip stuff is from \S 11.5 of Herbert Vo\ss's
% ``\href{http://www.ctan.org/tex-archive/info/math/voss/mathmode/}{Math
% Mode}''.
%    \begin{macrocode}
          tex_strs.append(r'\UseVerbatim{' + boxname + '}')
          try:
              result = eval(preparse(splitup[i][2]), globals, locals)
              tex_strs += [r'\abovedisplayskip=0pt plus 3pt ',
                           r'\abovedisplayshortskip=0pt plus 3pt ',
                           r'\begin{displaymath}',
                           latex(result),
                           r' \end{displaymath}']
          except SyntaxError:
              exec(preparse(splitup[i][2]), globals, locals)
      self.inline(counter, '\n'.join(tex_strs))
%    \end{macrocode}
% \changes{v2.2.5}{2010/03/25}{Fix up spacing in sageexample displaymath envs}
% \changes{v3.0}{2015/08/26}{sageexample and sagecommandline now require
% ``...:'' for continuation lines, not ``...''; matches the actual
% Sage interpreter}
% \end{macro}
%
% \begin{macro}{commandline}
%   This function handles the |commandline| environment, which typesets
%   Sage code, computes its output, and typesets that too. This is very
%   similar to |doctest| and I hope to someday combine them into one.
%
%   Even if I can't refactor these two functions (and their associated
%   environments) into one, I would like to eliminate the |.scmd| file
%   that this function uses, since exactly the same bits of Sage code
%   get written to both the |.scmd| file and the |_doctest.sage| file.
%   The reason this isn't trivial is because we need to keep track of
%   which line number we're on so that we can give the |listings|
%   package a start and end line to extract, and right now the
%   |_doctest.sage| file is written to by \LaTeX{} and we can't track
%   the line number.
%
%   In any case, here's what we do: after splitting up the provided
%   string using |split_sage_cmds|, we iterate over each of the
%   commands and:
%   \begin{enumerate}
%   \item Put the original input command into the |.scmd| file with
%     |savecmd|.
%   \item Use the |begin| and |end| line numbers to append a
%     |lstinputlisting| command to the \TeX{} commands we'll eventually
%     hand off to |inline|.
%   \item Evaluate the command using |eval()| or |exec|, as necessary.
%     If we're doing plain text format, we send the output to the
%     |.scmd| file and add a \TeX{} command to pull that back in---if we
%     need typeset output, then we just hit the output with |latex()|
%     and add that to the list of \TeX{} commands.
%   \end{enumerate}
%   Observe that we detect spaces in the filename and quote that for
%   \TeX{} if we need to.
%    \begin{macrocode}
  def commandline(self, counter, s, globals, locals, text_output):
      self.progress('Sage commandline {0} (line {1})'.format(counter, self.current_tex_line))
      scmd_fn = self.name + '.sagetex.scmd'
      if ' ' in scmd_fn:
          scmd_fn = '"{}"'.format(scmd_fn)

      splitup = self.split_sage_cmds(s)
      skip = r'\vspace{\sagecommandlineskip}'
      tex_strs = [skip]
      lstinput = r'\lstinputlisting[firstline={0},lastline={1},firstnumber={2},style=SageInput{escape}]{{{3}}}'
      for i in range(len(splitup)):
          orig_input = s[splitup[i][0]:splitup[i][1]]
          begin, end = self.savecmd(strip_common_leading_spaces(orig_input.strip('\n')))
          if '#@' in orig_input:
              escapeoption = ',escapeinside={\\#@}{\\^^M}'
          else:
              escapeoption = ''
          tex_strs.append(lstinput.format(begin, end, begin - 2, scmd_fn, escape=escapeoption))
          try:
              result = eval(preparse(splitup[i][2]), globals, locals)
              if text_output:
                  begin, end = self.savecmd(str(result))
                  tex_strs.append(lstinput.format(begin, end, begin - 2, scmd_fn, escape=''))
              else:
                  tex_strs.append(r'\begin{displaymath}' +
                                  latex(result) +
                                  r'\end{displaymath}')
          except SyntaxError:
              exec(preparse(splitup[i][2]), globals, locals)
      if 'displaymath' not in tex_strs[-1]:
          tex_strs.append(skip)
      self.inline(counter, '\n'.join(tex_strs), labelname='sagecmdline')
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{plot}
% \phantomsection\label{plotfn}
% I hope it's obvious that this function does plotting. It's the Python
% counterpart of |\ST@sageplot| described in \autoref{sec:sageplotmacro}. As
% mentioned in the |\sageplot| code, we're taking advantage of two
% things: first, that \LTX doesn't treat commas and spaces in macro
% arguments specially, and second, that Python (and Sage plotting
% functions) has nice support for keyword arguments. The |#3| argument
% to |\sageplot| becomes |_p_| and |**kwargs| below.
%    \begin{macrocode}
  def plot(self, counter, _p_, format='notprovided', **kwargs):
      if not self.didinitplot:
          self.initplot()
      self.progress('Plot {0} (line {1})'.format(counter, self.current_tex_line))
%    \end{macrocode}
% If the user says nothing about file formats, we default to producing
% PDF and EPS. This allows the user to transparently switch between
% using a DVI previewer (which usually automatically updates when the
% DVI changes, and has support for source specials, which makes the
% writing process easier) and making PDFs.\footnote{Yes, there's
% \texttt{pdfsync}, but full support for that is still rare in Linux, so
% producing EPS and PDF is the best solution for now.}
%    \begin{macrocode}
      if format == 'notprovided':
          formats = ['eps', 'pdf']
      else:
          formats = [format]
      for fmt in formats:
%    \end{macrocode}
% If we're making a PDF and have been told to use |epstopdf|, do so,
% then skip the rest of the loop.
%    \begin{macrocode}
          if fmt == 'pdf' and self.useepstopdf:
              epsfile = os.path.join(self.plotdir, 'plot-{0}.eps'.format(counter))
              self.progress('Calling epstopdf to convert plot-{0}.eps to PDF'.format(
                            counter))
              subprocess.check_call(['epstopdf', epsfile])
              continue
%    \end{macrocode}
% Some plot objects (mostly 3-D plots) do not support saving to EPS or
% PDF files (yet), but everything can be saved to a PNG file. For the
% user's convenience, we catch the error when we run into such an
% object, save it to a PNG file, then exit the loop.
%    \begin{macrocode}
          plotfilename = os.path.join(self.plotdir, 'plot-{0}.{1}'.format(counter, fmt))
          try:
              _p_.save(filename=plotfilename, **kwargs)
          except ValueError as inst:
              if re.match('filetype .*not supported by save', str(inst)):
                  newfilename = plotfilename[:-3] + 'png'
                  print('  saving {0} failed; saving to {1} instead.'.format(
                                                    plotfilename, newfilename))
                  _p_.save(filename=newfilename, **kwargs)
                  break
              else:
                  raise
%    \end{macrocode}
% If the user provides a format \emph{and} specifies the |imagemagick|
% option, we try to convert the newly-created file into EPS format.
%    \begin{macrocode}
          if format != 'notprovided' and self.useimagemagick:
              self.progress('Calling Imagemagick to convert plot-{0}.{1} to EPS'.format(
                counter, format))
              self.toeps(counter, format)
%    \end{macrocode}
% \end{macro}
%
% \begin{macro}{toeps}
% This function calls the Imagmagick utility |convert| to, well, convert
% something into EPS format. This gets called when the user has
% requested the ``|imagemagick|'' option to the \ST\ style file and is
% making a graphic file with a nondefault extension.
%    \begin{macrocode}
  def toeps(self, counter, ext):
    subprocess.check_call(['convert',\
      '{0}/plot-{1}.{2}'.format(self.plotdir, counter, ext), \
      '{0}/plot-{1}.eps'.format(self.plotdir, counter)])
%    \end{macrocode}
% We are blindly assuming that the |convert| command exists and will do
% the conversion for us; the |check_call| function raises an exception
% which, since all these calls get wrapped in try/excepts in the |.sage|
% file, should result in a reasonable error message if something strange
% happens.
% \end{macro}
%
% \begin{macro}{goboom}
% \phantomsection\label{macro:goboom}
% When a chunk of Sage code blows up, this function bears the bad news
% to the user. Normally in Python the traceback is good enough for
% this, but in this case, we start with a |.sage| file (which is
% autogenerated) which itself autogenerates a |.py| file---and the
% tracebacks the user sees refer to that file, whose line numbers are
% basically useless. We want to tell them where in the \LTX file
% things went bad, so we do that, give them the traceback, and exit
% after removing the |.sout.tmp| and |.scmd.tmp| file.
%    \begin{macrocode}
  def goboom(self, line):
    print('\n**** Error in Sage code on line {0} of {1}.tex! Traceback\
 follows.'.format(line, self.filename))
    traceback.print_exc()
    print('\n**** Running Sage on {0}.sage failed! Fix {0}.tex and try\
 again.'.format(self.filename))
    self.souttmp.close()
    os.remove(self.filename + '.sagetex.sout.tmp')
    self.scmdtmp.close()
    os.remove(self.filename + '.sagetex.scmd.tmp')
    sys.exit(int(1))
%    \end{macrocode}
% We use |int(1)| above to make sure |sys.exit| sees a Python integer;
% see
% \href{http://trac.sagemath.org/sage_trac/ticket/2861#comment:5}{ticket
% \#2861}.
% \changes{v2.0.2}{2008/04/21}{Make sure sys.exit sees a Python integer}
% \end{macro}
%
% \begin{macro}{endofdoc}
% \phantomsection\label{macro:endofdoc}
% When we're done processing, we have some cleanup tasks. We
% want to put the MD5 sum of the |.sage| file that produced the |.sout|
% file we're about to write into the |.sout| file, so that external
% programs that build \LTX documents can determine if they need to call Sage
% to update the |.sout| file. But there is a problem: we write line
% numbers to the |.sage| file so that we can provide useful error
% messages---but that means that adding non-\ST text to your
% source file will change the MD5 sum, and your program will think it
% needs to rerun Sage even though none of the actual \ST macros
% changed.
%
% How do we include line numbers for our error messages but still allow
% a program to discover a ``genuine'' change to the |.sage| file?
%
% The answer is to only find the MD5 sum of \emph{part} of the |.sage|
% file. By design, the source file line numbers only appear in (1) calls
% to |goboom|, (2) lines with |_st_.current_tex_line|, and (3)
% pause/unpause lines, so we will strip those lines out. What we do
% below is exactly equivalent to running
% \begin{center}
% \verb+egrep -v '^( _st_.goboom| ?_st_.current_tex_line|print(.SageT)' filename.sage | md5sum+
% \end{center}
% in a shell. The included |sagetex-run| uses this
% mechanism to, well, only run Sage when necessary; see
% \autoref{sec:sagetex-run}.
%    \begin{macrocode}
  def endofdoc(self):
    sagef = open(self.filename + '.sagetex.sage', 'r')
    m = hashlib.md5()
    for line in sagef:
      if not line.startswith((" _st_.goboom",
                              "print('SageT",
                              "_st_.current_tex_line",
                              " _st_.current_tex_line")):
          if PY3:
              m.update(bytearray(line,'utf8'))
          else:
              m.update(bytearray(line))
%    \end{macrocode}
% (The |current_tex_line| thing appears twice because it may appear
% indented one space or not, depending on whether it's used before
% |blockbegin| or not.)
%    \begin{macrocode}
    s = '%' + m.hexdigest() + '% md5sum of corresponding .sage file\
 (minus "goboom", "current_tex_line", and pause/unpause lines)\n'
    self.souttmp.write(s)
    self.scmdtmp.write(s)
%    \end{macrocode}
% Now, we do issue warnings to run Sage on the |.sage| file and an
% external program might look for those to detect the need to rerun
% Sage, but those warnings do not quite capture all situations. (If
% you've already produced the |.sout| file and change a |\sage| call, no
% warning will be issued since all the |\ref|s find a |\newlabel|.)
% Anyway, I think it's easier to grab an MD5 sum out of the end of the
% file than parse the output from running |latex| on your file. (The
% regular expression |^%[0-9a-f]{32}%| will find the MD5 sum. Note that
% there are percent signs on each side of the hex string.)
%
% Now we are done with the |.sout.tmp| file. Close it, rename it, and
% tell the user we're done.
%    \begin{macrocode}
    self.souttmp.close()
    os.rename(self.filename + '.sagetex.sout.tmp', self.filename + '.sagetex.sout')
    self.scmdtmp.close()
    os.rename(self.filename + '.sagetex.scmd.tmp', self.filename + '.sagetex.scmd')
    self.progress('Sage processing complete. Run LaTeX on {0}.tex again.'.format(
             self.filename))
%    \end{macrocode}
% % \changes{v2.1.1}{2009/05/14}{Fix bug in finding md5 sum introduced by
% pause facility}
% \end{macro}

% \endinput
%</python>
% Local Variables:
% mode: doctex
% TeX-master: "sagetex.dtx"
% End: