Setting an "attribute" for Theorem to be accessed later

Question

I am writing a math paper with a large number of theorems. I'm looking to have a table summarizing my results, and I'd love it if the table could be generated automatically from my paper. I' looking to be able to do something like this

\begin{thm}
 \shortTheorem{$x + y = y + x$}
 Let $x,y$ be integers. Then $x+y=y+x$.
 \end{thm}

Note that shortTheorem is just the name I made up for whatever tag I put my desired text into.

Then, later on, I want to have a table which, for each theorem I define, prints its "shortTheorem" contents. i.e.

• x + y = y + x

Are there existing packages to do this? If not, how would I go about writing my own macro to do so?

(Note: I couldn't figure out if there was a way to actually render a LaTeX table in my question, feel free to edit if you know how.)

Answer 1

This makes a table at the end, which is I think what you wanted:

\documentclass{article}

\makeatletter
\def\shortthms{}
\def\shorttheorem#1{\g@addto@macro\shortthms{#1\\}}
\makeatother

\newtheorem{thm}{Theorem}

\begin{document}



\begin{thm}
 \shorttheorem{$x + y = y + x$}
  Let $x,y$ be integers. Then $x+y=y+x$.
 \end{thm}

\begin{thm}
 \shorttheorem{$x + x = x + x$}
 Let $x,y$ be integers. Then $x+x=x+x$.
 \end{thm}


blab blah

\begin{tabular}{p{5cm}}
\shortthms
\end{tabular}

\end{document}

Plan b, using a file takes two latex runs to pull in the data:

\documentclass{article}

\makeatletter
%\def\shortthms{}
%\def\shorttheorem#1{\g@addto@macro\shortthms{#1\\}}

\def\shorttheorem#1{\immediate\write\shortthmout{\unexpanded{#1\\}}}


\def\shortthms{%
\begin{tabular}{p{5cm}}\@input{\jobname.thm}\end{tabular}%
\newwrite\shortthmout
\immediate\openout\shortthmout=\jobname.thm}

\makeatother

\newtheorem{thm}{Theorem}

\begin{document}


\shortthms



\begin{thm}
 \shorttheorem{$x + y = y + x$}
  Let $x,y$ be integers. Then $x+y=y+x$.
 \end{thm}

\begin{thm}
 \shorttheorem{$x + x = x + x$}
 Let $x,y$ be integers. Then $x+x=x+x$.
 \end{thm}


blab blah


\end{document}

Answer 2

If you want also to print the theorem number, here's a schematic solution:

\documentclass{article}
\usepackage{lipsum}% just for the example

\newcommand{\shorttheorem}[1]{%
  \xdef\shorttheoremlist{%
    \unexpanded\expandafter{\shorttheoremlist}%
    \noexpand\item[Theorem \thethm:]
    \unexpanded{#1}}}

\newcommand\shorttheoremlist{}
\newcommand\printshorttheorems{%
  \begin{description}
  \shorttheoremlist
  \end{description}}

\newtheorem{thm}{Theorem}

\begin{document}

\section{A section}

\lipsum[2]

\begin{thm}\shorttheorem{$x+y=y+x$}
Let $x$ and $y$ be integers. Then $x+y=y+x$.
\end{thm}

\lipsum[3]

\begin{thm}\shorttheorem{$\sqrt{x^2}=|x|$}
Let $x$ be an integer. Then $\sqrt{x^2}=|x|$.
\end{thm}

\section{The final list}

\printshorttheorems

\end{document}

Extended version

If you want to name the theorems in different ways and have them in the final list, then cleveref can come to the rescue. It's important to load also amsthm or ntheorem (I prefer the former) and to define the theorem-like environments after loading cleveref. Also, be sure to add the \shorttheorem bit at the start of the environment.

\documentclass{article}
\usepackage{lipsum}% just for the example

\usepackage{amsthm}
\usepackage{cleveref}

\newcommand{\shorttheorem}[1]{%
  \stepcounter{shortcount}%
  \label{shortcount\theshortcount}%
  \xdef\shorttheoremlist{%
    \unexpanded\expandafter{\shorttheoremlist}%
    \noexpand\item[\noexpand\Cref{shortcount\theshortcount}:]
    \unexpanded{#1}}}
\newcounter{shortcount}
\newcommand\shorttheoremlist{}
\newcommand\printshorttheorems{%
  \begin{description}
  \shorttheoremlist
  \end{description}}

\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}

\begin{document}

\section{A section}

\lipsum[2]

\begin{lem}\shorttheorem{$x+y=y+x$}
Let $x$ and $y$ be integers. Then $x+y=y+x$.
\end{lem}

\lipsum[3]

\begin{thm}\shorttheorem{$\sqrt{x^2}=|x|$}
Let $x$ be an integer. Then $\sqrt{x^2}=|x|$.
\end{thm}

\section{The final list}

\printshorttheorems

\end{document}

Extended version with arbitrary placement in the document

\documentclass{article}
\usepackage{lipsum}% just for the example

\usepackage{amsthm}
\usepackage{cleveref}

\makeatletter
\newwrite\shorttheoremfile
\newcounter{shortcount}
\newcommand{\shorttheorem}[1]{%
  \stepcounter{shortcount}%
  \label{shortcount\theshortcount}%
  \xdef\shorttheoremlist{%
    \unexpanded\expandafter{\shorttheoremlist}%
    \string\item[\string\Cref{shortcount\theshortcount}:]
    \unexpanded{#1}^^J}%
}
\newcommand{\shorttheoremlist}{}
\AtEndDocument{
  \immediate\openout\shorttheoremfile=\jobname.thm
  \immediate\write\shorttheoremfile{\unexpanded\expandafter{\shorttheoremlist}}
  \immediate\closeout\shorttheoremfile
}

\newcommand\printshorttheorems{%
  \begin{description}
  \def\@noitemerr{\@latex@warning{Empty short theorem list}}%
  \@input{\jobname.thm}
  \end{description}
}
\makeatother

\newtheorem{thm}{Theorem}
\newtheorem{lem}[thm]{Lemma}

\begin{document}

\section{Short theorems}

\printshorttheorems

\section{A section}

\lipsum[2]

\begin{lem}\shorttheorem{$x+y=y+x$}
Let $x$ and $y$ be integers. Then $x+y=y+x$.
\end{lem}

\lipsum[3]

\begin{thm}\shorttheorem{$\sqrt{x^2}=|x|$}
Let $x$ be an integer. Then $\sqrt{x^2}=|x|$.
\end{thm}

\end{document}