我可以对假设进行编号以与后续定理相一致吗？

Question

我有 TeX，它使用 定义theorem和assumption环境\newtheorem，并且它在每个定理之后正确地重置假设计数器。

编号现在方法：

• 假设 0.1 和 0.2 与定理 1 相关
• 假设 1.1 和 1.2 与定理 2 相关

但那很尴尬。更好的如果编号如下：

• 假设 1.1 和 1.2 与定理 1 相关
• 假设 2.1 和 2.2 与定理 2 相关

有没有合理的方法来实现这一点？

特克斯：

\newtheorem{theorem}{Theorem}
\newtheorem{assumption}{Assumption}[theorem]

\begin{document}


\begin{assumption} \label{a}
    Object $\mathcal{A}$ is great.
\end{assumption}

\begin{assumption} \label{b}
    Object $\mathcal{B}$ is truly wonderful.
\end{assumption}

\begin{theorem}
    Subject to Assumptions \ref{a} and \ref{b}, $\mathcal{A} \bigoplus \mathcal{B} = \mathcal{B}$.
\end{theorem}


\begin{assumption} \label{aa}
    Object $\mathfrak{A}$ is awful.
\end{assumption}

\begin{assumption} \label{bb}
    Object $\mathfrak{B}$ is truly terrible.
\end{assumption}

\begin{theorem}
    Subject to Assumptions \ref{aa} and \ref{bb}, $\mathfrak{A} \bigotimes \mathfrak{B} = \mathfrak{B}$.
\end{theorem}


\end{document}

如果我在开始时使用\setcounter计数器assumption，它会将 N 更改为 0.N。如果我\setcounter{theorem}{1}在开始时使用，则问题仍然存在，只是偏移了 1。

Answer 1

DIY \theassumption，并强制其加1。

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}

\newtheorem{theorem}{Theorem}
\newtheorem{assumption}{Assumption}[theorem]


%%%% THE KEY LINE BELOW
\renewcommand\theassumption{\the\numexpr\thetheorem + 1\relax.\arabic{assumption}}
%%%%

\begin{document}


\begin{assumption} \label{a}
    Object $\mathcal{A}$ is great.
\end{assumption}

\begin{assumption} \label{b}
    Object $\mathcal{B}$ is truly wonderful.
\end{assumption}

\begin{theorem}
    Subject to Assumptions \ref{a} and \ref{b}, $\mathcal{A} \bigoplus \mathcal{B} = \mathcal{B}$.
\end{theorem}


\begin{assumption} \label{aa}
    Object $\mathfrak{A}$ is awful.
\end{assumption}

\begin{assumption} \label{bb}
    Object $\mathfrak{B}$ is truly terrible.
\end{assumption}

\begin{theorem}
    Subject to Assumptions \ref{aa} and \ref{bb}, $\mathfrak{A} \bigotimes \mathfrak{B} = \mathfrak{B}$.
\end{theorem}


\end{document}

（请注意，这假设您希望始终以阿拉伯数字形式打印定理数字。）

Answer 2

您可以定义一个assumption环境，将其所引用的定理的标签作为参数。

\documentclass{article}
\usepackage{amsmath,amssymb}
\usepackage{amsthm}
\usepackage{refcount}
%\usepackage{hyperref}

\newtheorem{theorem}{Theorem}

\newtheorem{assumptioninner}{Assumption}
\newcounter{assumption}
\newenvironment{assumption}[1]
 {% #1 is the label of the corresponding theorem
  \ifcsname assumption@#1\endcsname
    % not the first assumption, advance
    \expandafter\xdef\csname assumption@#1\endcsname{%
      \the\numexpr\csname assumption@#1\endcsname+1\relax
    }%
  \else
    \expandafter\xdef\csname assumption@#1\endcsname{1}%
  \fi
  \renewcommand{\theassumptioninner}{\getrefnumber{#1}.\csname assumption@#1\endcsname}%
  \assumptioninner
 }
 {\endassumptioninner}

\begin{document}

\begin{assumption}{first}\label{a}
    Object $\mathcal{A}$ is great.
\end{assumption}

\begin{assumption}{first}\label{b}
    Object $\mathcal{B}$ is truly wonderful.
\end{assumption}

\begin{assumption}{second}\label{aa}
    Object $\mathfrak{A}$ is awful.
\end{assumption}

\begin{theorem}\label{first}
    Subject to Assumptions \ref{a} and \ref{b},
    $\mathcal{A} \bigoplus \mathcal{B} = \mathcal{B}$.
\end{theorem}

\begin{assumption}{second}\label{bb}
    Object $\mathfrak{B}$ is truly terrible.
\end{assumption}

\begin{theorem}\label{second}
    Subject to Assumptions \ref{aa} and \ref{bb},
    $\mathfrak{A} \bigotimes \mathfrak{B} = \mathfrak{B}$.
\end{theorem}

\end{document}

我相信可能有一种方法可以根据以下定理自动对假设进行编号。如果假设不需要仅先于它们引用的定理，那就不行。

该代码已经过带有和不带有的测试hyperref。