如您所知,在 latex 中可以创建一个快捷方式列表(如公式)并在文档/书籍正文中调用它。我想知道是否可以对定义/引理/证明做类似的事情。就像说...创建一个包含所有证明的文件,给它们贴上标签,当我引用标签时,只需将证明正文替换为标签即可。
那可能吗?
我将使用以下示例来解释我想要实现的目标:
\begin{definition}
We define the set of normalized floating point numbers $\FloatingPointSet{e}{t}$ as
\begin{equation}
\FloatingPointSet{e}{t} = \left\{x \in \mathbb{R} \; : \;
\left\{
\begin{array}{l}
x = (-1)^{s_x} 2^{e_x} 1.m_x, \\
s_x \in {0,1} \\
2 - 2^{e - 1} \leq e_x \leq 2^{e-1}-1 \\
1.m_x = \sum_{i=0}^{t} x_{-j} 2^{-j} \\
x_0 = 1
\end{array}
\right.
\right\}.
\label{eq:floatingPointSetDef}
\end{equation}
\label{def:floatingPointSetDef}
\end{definition}
\begin{proposition}
For each $x \in \FloatingPointSet{e}{t}$ we can write
\begin{equation}
x = (-1)^{s_x} 2^{e_x - t} M_x,
\label{eq:floatingPointIntegerSignificand}
\end{equation}
where $2^t \leq M_x \leq 2^{t+1} - 1$
\end{proposition}
\begin{proof}
\begin{multline}
x = (-1)^{s_x} 2^{e_x} 1.m_x = (-1)^{s_x} 2^{e_x} \sum_{i=0}^{t} x_{-j}2^{-j} = \\
(-1)^{s_x} 2^{e_x-t} \sum_{i=0}^{t} x_{-j}2^{t-j} = (-1)^{s_x} 2^{e_x-t} M_x
\end{multline}
where $M_x$ is defined as
\begin{equation}
M_x = \sum_{i=0}^{t}x_{-j}2^{t-j}
\end{equation}
since $x_0 = 1$ then $2^t \leq M_x$, so $2^t$ is the lower bound, for the upper bound we just put $x_{-j} = 1 \;\; \forall j = 1 \ldots t$ so the upper bound is $2^{t+1} - 1$.
\end{proof}
\begin{definition}
For each $x \in \FloatingPointSet{e}{t}$ we define
\begin{equation}
\text{ulp}\left( x \right) = 2^{e_x - t}
\end{equation}
\end{definition}
我的想法是......
把这些内容放在一个文件中,例如:
\begin{defintion}
%text def
\label{def1}
\end{definition}
\begin{lemma}
%text lemma
\label{lemma1}
\end{lemma}
\begin{proof}
%text def
\label{proof1}
\end{proof}
在单个文件中...然后在文档的实际主体中(在不同的文件中)我希望能够执行以下操作:
The following defintion is useful and summarizes what we explained so far
\ref{def1},
it is easy to see that the following lemma holds
\ref{lemma1}
\ref{proof1}
所以实际上我想避免将所有证明与文档文本一起放在一个文件中,因为当我必须挖掘文档以查找错误时,这会让我感到困惑。这样可以吗?