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定理会用在什么地方？

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定理会用在什么地方？

我曾经看过一本书（Reinhard Diestel 的《图论》），作者在书页的左侧/右侧标记了后面将应用该定理的定理的参考编号。真正的双向交叉引用！

我认为这是自动完成的，但是如何完成呢？我从未见过这样的包。

以下是屏幕截图：

迪斯特尔书中的截图

答案1

refthm_输出

更新 2

refprop在此更新中，我消除了需要引用时需要使用另一个环境的缺陷。现在，您可以使用原始定理环境（ prop）作为\begin{prop}[<specification>][<label>]（参见下面的代码）。解决方案必须由触发\RefthmPatch{<list of your thm-envs>}

\documentclass{book}
\usepackage[margin=3cm,marginparwidth=2cm]{geometry}
\usepackage{lipsum}
\usepackage{marginnote}
\usepackage{etoolbox}
\usepackage{twoopt}
\usepackage{amsthm}
  \newtheorem{prop}{Proposition}[section]
% \newtheorem{thm}{Theorem}[section]
% \newtheorem{lem}{Lemma}[section]

\makeatletter
\newcommand{\do@patch@refthm}[1]{%
  \expandafter\let\csname svd@#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\renewcommandtwoopt\csname #1\endcsname[2][][]{%
    \csname svd@#1\endcsname[##1]
    \if\relax\detokenize{##2}\relax\else
      \marginnote{\centering\normalfont\lbrack\ref{##2}\rbrack}\fi}}
\def\@patch@refthm@list{}
\newcommand{\RefthmPatch}[1]{\gdef\@patch@refthm@list{#1}}
\AtBeginDocument{%
  \let\do=\do@patch@refthm
  \expandafter\docsvlist\expandafter{\@patch@refthm@list}}
\makeatother

\RefthmPatch{prop}
%If you use more theorems:
%\RefthmPatch{thm,prop,lem}

\begin{document}
%%%%%%%%%%%%%%%%%%%%
\makeatletter
  \c@chapter=1
  \c@section=9
  \c@prop=2
\makeatother
%%%%%%%%%%%%%%%%%%%%
\mbox{}
\clearpage
\lipsum[1-4]
\begin{prop}[][somethm:1]
  Together with $\emptyset$ the cuts in $G$ from a subspace $\mathcal{C}^*$ of $\mathcal{E}(G)$. This space is generated by cuts of the form $E(v)$.
\end{prop}
\lipsum[5-8]
...
%%%%%%%%%%%%%%%%%%%%
\makeatletter
  \c@chapter=4
  \c@section=6
  \c@prop=2
\makeatother
%%%%%%%%%%%%%%%%%%%%
\begin{prop}\label{somethm:1}
  A Theorem in which a certain theorem is used.
\end{prop}
\end{document}

更新 1

我稍微修改了之前的方法。现在的解决方案可以做到：

\documentclass{book}
\usepackage[margin=3cm,marginparwidth=2cm]{geometry}
\usepackage{lipsum}
\usepackage{marginnote}
\usepackage{amsthm}

\newtheorem{prop}{Proposition}[section]

\newenvironment{refprop}[1]
  {\begin{prop}\marginnote{\centering\normalfont\lbrack\ref{#1}\rbrack}}
  {\end{prop}}

\begin{document}
%%%%%%%%%%%%%%%%%%%%
\makeatletter
  \c@chapter=1
  \c@section=9
  \c@prop=2
\makeatother
%%%%%%%%%%%%%%%%%%%%
\mbox{}
\clearpage
\lipsum[1-4]
\begin{refprop}{somethm:1}
Together with $\emptyset$ the cuts in $G$ from a subspace $\mathcal{C}^*$ of $\mathcal{E}(G)$. This space is generated by cuts of the form $E(v)$.
\end{refprop}
\lipsum[5-8]
...
%%%%%%%%%%%%%%%%%%%%
\makeatletter
  \c@chapter=4
  \c@section=6
  \c@prop=2
\makeatother
%%%%%%%%%%%%%%%%%%%%
\begin{prop}\label{somethm:1}
A Theorem in which a certain theorem is used.
\end{prop}
\end{document}

评论

下一步是将其应用于给定的一组定理环境。对于该任务，可以编写包装器。但这不是答案的范围。

原始解决方案

尽管这\vskip有点困扰我，因为它是任意的，但这可能会起作用：

\reversemarginpar

\newenvironment{refthm}[1]
  {\marginpar[\centering\vskip3mm\lbrack\ref{#1}\rbrack]{}\begin{somethmenv}}
  {\end{somethmenv}}


\begin{refthm}{somethm:1}
A theorem which will be applied in a later theorem with the label somethm:1.
\end{refthm}

...

\begin{someotherthmenv}\label{somethm:1}
A Theorem in which a certain theorem is used.
\end{someotherthmenv}

答案2

这是我的“廉价 Diestel”答案，因为我的解决方案只是将所有边距文本放在右侧，而不是检查页面是否应该放在左侧/右侧。对我来说，这已经足够好了，因为我不会打印出我的文档。

我的诀窍是简单地使用marginpar。关键的代码行是：

\newcommand{\margin}[1]{\marginpar{\flushright \textcolor{blue}{\small{#1}}}}。

最小工作示例：

\documentclass{article}
\usepackage[utf8]{inputenc}
\usepackage{amsmath, amsthm}
\usepackage[]{geometry}
\newtheorem{theorem}{Theorem}[section]
\theoremstyle{definition}
\newtheorem{definition}[theorem]{Definition}

\usepackage[colorlinks=true,
            linkcolor=blue, 
            citecolor=blue, 
            allcolors=blue]{hyperref}
\newcommand{\margin}[1]{\marginpar{\flushright \textcolor{blue}{\small{#1}}}}

\begin{document}
\begin{theorem}[Hall's] \label{theorem1} 
  Let $G = (A, B)$ be a bipartite graph. 
  Then $G$ has a matching \margin{bipartite} if and only if 
  $|N_G(S)| \geq |S|$ for all $S \subseteq A$ \margin{$N_G(S)$}. 
\end{theorem}

\begin{theorem}[Tutte's] \label{theorem2} 
  Let $G$ be a graph. 
  Then $G$ has a matching if and only if $q(G-S) \leq |S|$ 
  for all $S \subseteq V(G)$. \margin{$q$, [\ref{theorem3}]}
\end{theorem}
This is a strengthening of Theorem \ref{theorem1}.

\begin{theorem}[Gallai-Edmonds] \label{theorem3} 
  Every \margin{[\ref{theorem2}]} graph $G$ contains 
  $S \subseteq V(G)$ with the following two properties:
  \begin{enumerate}
    \item $S$ is matchable to $G-S$, \margin{matchable}
    \item Every component of $G-S$ is 
          factor critical. \margin{factor 
  critical}
  \end{enumerate}
  Given $S$ satisfying the following two properties,  
  $G$ contains a $1$-factor if and only if 
  $|S| = |\mathcal{C}_{G-S}|$. \margin{$\mathcal{C}_{G-S}$}
\end{theorem}
\end{document}

输出结果如下： 在此处输入图片描述 请注意，您还需要该hyperref包来使引用也可点击。

我尽可能地模仿 Diestel，因此如果一切设置正确，方括号中的参考文献应该是可点击的，并引导您找到正确的定理，就像正常引用一样。

当然，您可以在\newcommand{\margin}[1]{\marginpar{\flushright \textcolor{blue}{\small{#1}}}}命令中更改颜色、大小或字体系列。

不幸的是，我无法自动完成此操作。

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