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如何使这些数学段落更具可读性？

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如何使这些数学段落更具可读性？

我在分隔数学文本的段落时遇到了困难，例如输出中的第 8-9 行之间。一种选择是在每个新段落的第一句开头留出空格。

代码

\documentclass{article}

\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\usepackage{polyglossia} % also loads package fontspec

%% http://tex.stackexchange.com/q/43648/13173
\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
  \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
  \renewenvironment{#1}%
     {\linenomath\csname old#1\endcsname}%
     {\csname oldend#1\endcsname\endlinenomath}}% 
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
  \patchAmsMathEnvironmentForLineno{#1}%
  \patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\NewDocumentCommand{\normL}{ s O{} m }{%
  \IfBooleanTF{#1}{\norm*{#3}}{\norm[#2]{#3}}_{L_2(\Omega)}%
}

\usepackage{enumitem}   
\linenumbers
\begin{document}

\begin{enumerate}
\item % do not use an empty line here 
\begin{enumerate}[label={(\alph*)}]
\item Recall that

Then, $c_{0}$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
$\norm{u}_{l^{\infty}} 
= \sup\nolimits_{ j \in \mathbb{N} } \abs{ u_{j} } 
\,\,\, \forall u 
= (u_{j})_{j \in \mathbb{N}} \in c_{0} \text{ or } c$. 

For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 ... 0.1.0...) \in l_{p}$ (1 in the $n^{th}$ position). 
The notation is used for the space $c_{0}$. 
Also, for $X = l_{p}$ with $1 \leq p < \infty,$ or $c_{0}$, we define the canonical projections 
$(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
X \to \mathbb{K}, p_{n} (u_1, ..., u_{n}, ...) 
= u_{n} 
\, \forall (u_{1}, ..., u_{j}, ...) \in X$. 

For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
$l_{p}^{j} = ( \mathbb{K}^{n}, \norm{ \cdot }_{p} )$, 
where 
$\norm{ (u_{1}, ..., u_{n}) }_{p} 
= (\sum\nolimits_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
for $1 \leq p < \infty$ 
and 
$\norm{ (u_{1}, ..., u_{n} ) }_{\infty} 
= \max\nolimits_{1 \leq k \leq j} \abs{u_{k}}$. 

\end{enumerate}
\end{enumerate}    
\end{document}

输出

在此处输入图片描述

评论

  • 我在文中使用\nolimits使得句子更好地保持行高。
  • 从第 5 行和第 9 行开始的段落很难与其他文本区分开。

如何才能使文本更易读？我认为最好将段落分开（通过在段落开头添加空格是一种选择）。

答案1

latex 列表中的段落间距称为\parsep。由于您已经在使用，enumitem可以使用选项进行设置parsep。此外，正如评论中所述，您不需要\nolimits这里，

在此处输入图片描述

\documentclass{article}

\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\usepackage{polyglossia} % also loads package fontspec

%% http://tex.stackexchange.com/q/43648/13173
\newcommand*\patchAmsMathEnvironmentForLineno[1]{%
  \expandafter\let\csname old#1\expandafter\endcsname\csname #1\endcsname
  \expandafter\let\csname oldend#1\expandafter\endcsname\csname end#1\endcsname
  \renewenvironment{#1}%
     {\linenomath\csname old#1\endcsname}%
     {\csname oldend#1\endcsname\endlinenomath}}% 
\newcommand*\patchBothAmsMathEnvironmentsForLineno[1]{%
  \patchAmsMathEnvironmentForLineno{#1}%
  \patchAmsMathEnvironmentForLineno{#1*}}%
\AtBeginDocument{%
\patchBothAmsMathEnvironmentsForLineno{equation}%
\patchBothAmsMathEnvironmentsForLineno{align}%
\patchBothAmsMathEnvironmentsForLineno{flalign}%
\patchBothAmsMathEnvironmentsForLineno{alignat}%
\patchBothAmsMathEnvironmentsForLineno{gather}%
\patchBothAmsMathEnvironmentsForLineno{multline}%
}

\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\NewDocumentCommand{\normL}{ s O{} m }{%
  \IfBooleanTF{#1}{\norm*{#3}}{\norm[#2]{#3}}_{L_2(\Omega)}%
}

\usepackage{enumitem}   
\linenumbers
\begin{document}

\begin{enumerate}
\item % do not use an empty line here 
\begin{enumerate}[label={(\alph*)},parsep=\medskipamount]
\item Recall that

Then, $c_{0}$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
$\norm{u}_{l^{\infty}} 
= \sup_{ j \in \mathbb{N} } \abs{ u_{j} } 
\,\,\, \forall u 
= (u_{j})_{j \in \mathbb{N}} \in c_{0} \text{ or } c$. 

For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 ... 0.1.0...) \in l_{p}$ (1 in the $n^{th}$ position). 
The notation is used for the space $c_{0}$. 
Also, for $X = l_{p}$ with $1 \leq p < \infty,$ or $c_{0}$, we define the canonical projections 
$(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
X \to \mathbb{K}, p_{n} (u_1, ..., u_{n}, ...) 
= u_{n} 
\, \forall (u_{1}, ..., u_{j}, ...) \in X$. 

For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
$l_{p}^{j} = ( \mathbb{K}^{n}, \norm{ \cdot }_{p} )$, 
where 
$\norm{ (u_{1}, ..., u_{n}) }_{p} 
= (\sum_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
for $1 \leq p < \infty$ 
and 
$\norm{ (u_{1}, ..., u_{n} ) }_{\infty} 
= \max_{1 \leq k \leq j} \abs{u_{k}}$. 

\end{enumerate}
\end{enumerate}    
\end{document}

答案2

有标准的垂直空格：\smallskip、\medskip和\bigskip。使用它们（在本例中可能是第一个）可以为创建段落提供一些灵活性。

我假设您不想\parskip在全球范围内设置某个正值，这可能是一种替代方法。

输出 two\smallskip和 one \medskip：

在此处输入图片描述

答案3

您可以在枚举中定义更大的行距。虽然不太美观，但如果您认为这有助于提高可读性，那就好了。

% arara: pdflatex

\documentclass{article}
\usepackage{mathtools,amssymb}
\usepackage[mathlines]{lineno} 
\DeclarePairedDelimiter{\abs}{\lvert}{\rvert}
\DeclarePairedDelimiter{\norm}{\lVert}{\rVert}
\usepackage{enumitem}   
\linenumbers
\usepackage{setspace}
\usepackage{blindtext}

\begin{document}
\blindtext  
\begin{enumerate}
    \item 
        \begin{enumerate}[label={(\alph*)}]\setstretch{1.1}
            \item Recall that\par           
            Then, $c_0$ and $c$ are linear spaces with respect to the natural operations for addition and scalar multiplication and Banach spaces with respect to the norm 
            $\norm{u}_{l^{\infty}} 
            = \sup\nolimits_{ j \in\mathbb{N}} \abs{u_j}\ \forall u 
            = (u_{j})_{j \in \mathbb{N}} \in c_{0}$ or $c$.\par         
            For $1 \leq p < +\infty$ and $n \in \mathbb{N}$, we denote $e_{n} = (0 \dots 0.1.0\dots) \in l_{p}$ ($1$ in the $n$th position). 
            The notation is used for the space $c_0$. 
            Also, for $X = l_{p}$ with $1 \leq p < \infty$, or $c_{0}$, we define the canonical projections 
            $(p_{j})_{j \in \mathbb{N}} \cdot p_{n} : 
            X \to \mathbb{K}, p_{n} (u_1,\dots, u_{n},\dots) = u_{n}\ \forall (u_{1},\dots, u_{j},\dots) \in X$.\par
            For $n \in \mathbb{N}$ and $1 \leq p \leq +\infty$, we denote 
            $l_{p}^{j} = ( \mathbb{K}^{n}, \norm{\cdot}_{p} )$, 
            where 
            $\norm{ (u_{1},\dots, u_{n})}_{p} 
            = (\sum\nolimits_{k=1}^{n} \abs{u_{k}}^{p} )^{1/p}$ 
            for $1 \leq p < \infty$ 
            and 
            $\norm{ (u_{1},\dots, u_{n})}_{\infty} 
            \linebreak = \max\nolimits_{1 \leq k \leq j} \abs{u_{k}}$.          
        \end{enumerate}
\end{enumerate}  
\blindtext  
\end{document}

在此处输入图片描述

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