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a/learning_LaTeX.tex b/learning_LaTeX.tex index 687a080..f071d6c 100644 --- a/learning_LaTeX.tex +++ b/learning_LaTeX.tex @@ -11,11 +11,14 @@ \usepackage{graphicx} \usepackage{subfig} \usepackage{amsmath,amsfonts,amssymb,amsthm} +\usepackage{amsbsy} \usepackage{latexsym} \usepackage{float} \DeclareMathOperator{\argh}{argh} \DeclareMathOperator*{\nut}{Nut} \usepackage{yhmath} +\usepackage{eucal,mathrsfs} + \begin{document} \title{标题页} @@ -49,6 +52,7 @@ And I think this is: supercalifragilisticexpialidocious.\par \newpage \tableofcontents + \newpage \section[目录和页眉页脚]{章节} \subsection{子章节} \subsubsection{子子章节} @@ -561,9 +565,14 @@ \caption{文本/数学模式通用符号} \begin{tabular}{clclclcl} \hline - \{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\ + \{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\ \dag & \textbackslash dag & \S & \textbackslash S & \copyright & \textbackslash copyright & \dots & \textbackslash dots \\ - \ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds \\ + \ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds & \S & \textbackslash S \\ + \textasteriskcentered & \textbackslash textasteriskcentered & + \textperiodcentered & \textbackslash textperiodcentered & + \textbullet & \textbackslash textbullet \\ + \textregistered{} & \textbackslash textregistered{} & + \texttrademark & \textbackslash texttrademark \\ \hline \end{tabular} \end{table} @@ -1050,7 +1059,317 @@ \bigg\Downarrow \Bigg\Downarrow \] \subsection{多行公式} - + \subsubsection{长公式折行} + amsmath 宏包的 multline 环境提供了书写折行长公式的方便环境。它允许用 % + \textbackslash\textbackslash 折行,将 公式编号放在最后一行。% + 多行公式的首行左对齐,末行右对齐,其余行居中。 + \begin{multline} + a + b + c + d + e + f + g + h + i\\ + = j + k + l + m + n\\ + = o + p + q + r + s\\ + = t + u + v + w + x + \end{multline} + 类似 equation*,multline* 环境排版不带编号的折行长公式。 + \subsubsection{多行公式} + 罗列一系列公式,并令其按照等号对齐。\\ + 目前最常用的是 align 环境,它将公式用 \& 隔为两部分并对齐。分隔符通常放在等号左边: + \begin{align} + a & = b + c \\ + & = d + c + \end{align} + align 环境会给每行公式都编号。我们仍然可以用 \textbackslash notag 去掉某行的编号。\\ + 为了对齐加号,我们将分隔符放在等号右边,这时需要给等号后添加一对括号 \{\} 以产生正常的 间距: + \begin{align} + a ={} & b + c \\ + ={} & d + e + f + g + h + i + j + k + l \notag \\ + & + m + n + o \\ + ={} & p + q + r + s + \end{align} + align 还能够对齐多组公式,除等号前的 \& 之外,公式之间也用 \& 分隔: + \begin{align} + a & = 1 & b & = 2 & c & = 3 \\ + d & = - 1 & e & = - 2 & f & = - 5 + \end{align} + 如果我们不需要按等号对齐,只需罗列数个公式,gather 将是一个很好用的环境: + \begin{gather} + a = b + c \\ + d = e + f + g \\ + h + i = j + k \\ + l + m = n + \end{gather} + align 和 gather 有对应的不带编号的版本 align* 和 gather* + \subsubsection{公用编号的多行公式} + 多个公式组在一起公用一个编号,编号位于公式的居中位置。\\ + amsmath 宏包提供了诸如 aligned、gathered 等环境,% + 与 equation 环境套用。以 -ed 结尾的环境用法与前一节不以 -ed 结尾的环境用法一一对应。 + \begin{equation} + \begin{aligned} + a & = b + c \\ + d & = e + f + g \\ + h + i & = j + k \\ + l + m & = n + \end{aligned} + \end{equation} + split 环境和 aligned 环境用法类似,也用于和 equation 环境套用,区别是 split 只能 将每行的一个公式分两栏, + aligned 允许每行多个公式多栏。 + \subsection{数组和矩阵} + 二维数组,\LaTeX 提供了 array 环境,用法与 tabular 环境极为类似,% + 也需要定 义列格式,并用 \textbackslash \textbackslash 换行。% + 数组可作为一个公式块,在外套用 \textbackslash left、\textbackslash right 等定界符: + \[ + \mathbf{X} = \left( + \begin{array}{cccc} + x_{11} & x_{12} & \ldots & x_{1n} \\ + x_{21} & x_{22} & \ldots & x_{2n} \\ + \vdots & \vdots & \ddots & \vdots \\ + x_{n1} & x_{n2} & \ldots & x_{nn} + \end{array} + \right) + \] + amsmath 提供的 cases 环境 + \[ + |x| = + \begin{cases} + - x & \text{if } x < 0, \\ + 0 & \text{if } x = 0, \\ + x & \text{if } x > 0. + \end{cases} + \] + amsmath 宏包提供了多种排版矩阵的环境,包括不带定界符的 matrix,以及带各种定界符的矩阵 pmatrix ($\left(\right.$) 、 + bmatrix ($\left[\right.$) 、 Bmatrix ($\left\{\right.$) 。使用这些环境时,无需给定列格式 : + \[ + \begin{matrix} + 1 & 2 \\ + 3 & 4 + \end{matrix} \qquad + \begin{bmatrix} + x_{11} & x_{12} & \ldots & x_{1n} \\ + x_{21} & x_{22} & \ldots & x_{2n} \\ + \vdots & \vdots & \ddots & \vdots \\ + x_{n1} & x_{n2} & \ldots & x_{nn} + \end{bmatrix} + \] + 在矩阵中的元素里排版分式时,一来要用到 \textbackslash dfrac 等命令,% + 二来行与行之间有可能紧贴着, 这时要调节间距: + \[ + \mathbf{H} = + \begin{bmatrix} + \dfrac{\partial^2 f}{\partial x^2} & \dfrac{\partial^2 f}{\partial x\partial y} \\[8pt] + \dfrac{\partial^2 f}{\partial x\partial y} & \dfrac{\partial^2 f}{\partial y^2} + \end{bmatrix} + \] + \subsection{公式中的间距} + 生成间距的命令 \textbackslash quad 和 \textbackslash qquad 和 \textbackslash , 在文本和数学 环境中可用\\ + \textbackslash ,、\textbackslash :、\textbackslash ; 以及负间距 \textbackslash ! % + 命令只用于数学环境。文本中的 \textbackslash\verb*| | 也能使用在数学公式中。\par + \begin{table}[H] + \centering + \begin{tabular}{ll|ll} + \hline + 无额外间距 & aa & + \textbackslash , & a\,a \\ + \textbackslash quad & a\quad a & + \textbackslash : & a\:a \\ + \textbackslash qquad & a\qquad a & + \textbackslash ; & a\;a \\ + \textbackslash \verb*| | & a\ a & + \textbackslash ! & a\!a \\ + \hline + \end{tabular} + \end{table} + 一个常见的用途是修正积分的被积函数 $f(x)$ 和微元 $\text{d}x$ 之间的距离。 + \[ + \int_a^b f(x) \mathrm{d}x + \qquad + \int_a^b f(x) \, \mathrm{d}x + \] + 另一个用途是生成多重积分号。如果我们直接连写两个 \textbackslash int,% + 之间的间距将会过宽,此时 可以使用负间距 \textbackslash ! 修正之。 + \begin{gather*} + \int\int f(x)g(y) \,\mathrm{d}x\,\mathrm{d}y \\ + \int\!\!\!\int f(x)g(y) \mathrm{d}\,x\mathrm{d}\,y + \end{gather*} + amsmath 提供了更方便的多重积分号,如二重积分 \textbackslash iint、% + 三 重积分 \textbackslash iiint 等。 + \begin{gather*} + \iint f(x)g(y) \,\mathrm{d}x\,\mathrm{d}y \\ + \iint \quad \iiint \quad \idotsint + \end{gather*} + \subsection{数学符号的字体控制} + \subsubsection{数学字母字体} + \begin{table}[H] + \centering + \caption{数学字母字体} + \begin{tabular}{lll} + \toprule + 示例 &命令 &依赖的宏包\\ + \midrule + $\mathnormal{ABCDEabcde1234}$ & \textbackslash mathnormal\{\ldots\} & \\ + $\mathrm{ABCDEabcde1234}$ & \textbackslash mathrm\{\ldots\} & \\ + $\mathit{ABCDEabcde1234}$ & \textbackslash mathit\{\ldots\} & \\ + $\mathbf{ABCDEabcde1234}$ & \textbackslash mathbf\{\ldots\} & \\ + $\mathsf{ABCDEabcde1234}$ & \textbackslash mathsf\{\ldots\} & \\ + $\mathtt{ABCDEabcde1234}$ & \textbackslash mathtt\{\ldots\} & \\ + $\mathcal{ABCDEabcde1234}$ & \textbackslash mathcal\{\ldots\} & 只大写字母 \\ + \midrule + $\mathcal{ABCDE}$ & \textbackslash mathcal\{\ldots\} & eucal,只大写字母 \\ + $\mathscr{ABCDE}$ & \textbackslash mathscr\{\ldots\} & mathrsfs,只大写字母 \\ + $\mathfrak{ABCDEabcde1234}$ & \textbackslash mathfrak\{\ldots\} & amssymb 或 eufrak \\ + $\mathbb{ABCDE}$ & \textbackslash mathbb\{\ldots\} & amssymb,只大写字母 \\ + \bottomrule + \end{tabular} + \end{table} + \[ \mathcal{R} \quad \mathfrak{R \quad \mathbb{R}} \] + \[ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} \] + $\mathfrak{su}(2)$ and $\mathfrak{so}(3)$ Lie algebra + \subsubsection{数学符号的尺寸} + \begin{table}[H] + \centering + \caption{数学符号尺寸} + \begin{tabular}{lll} + \toprule + 命令 &尺寸 &示例\\ + \midrule + \textbackslash displaystyle & 行间公式尺寸 & $\displaystyle \sum a$ \\ + \textbackslash textstyle & 行内公式尺寸 & $\textstyle \sum a$ \\ + \textbackslash scriptstyle & 上下标尺寸 & $\scriptstyle a$ \\ + \textbackslash scriptscriptstyle & 次级上下标尺寸 & $\scriptscriptstyle a$ \\ + \bottomrule + \end{tabular} + \end{table} + \[ + P = \frac + {\sum_{i = 1}^n (x_i - x)(y_i - y)} + {\displaystyle \left[ + \sum_{i = 1}^n (x_i - x)^2 + \sum_{i = 1}^n (y_i - y)^2 + \right]^{1/2}}\, + \] + \subsubsection{加粗的数学符号} + \LaTeX 提供了一个命令 \textbackslash boldmath 令用户可以将整套数学字体切换为粗体版本。但这个命 令只能在公式外使用:\par + $\mu, M \qquad \mathbf{\mu}, \mathbf{M}$ \qquad + {\boldmath$\mu, M$\par} + amsmath 提供了一个 \textbackslash boldsymbol 命令(由调用的 amsbsy 宏包提供) ,% + 用于打破 \textbackslash boldmath 的限制,在公式内部将一部分符号切换为粗体。\par + $\mu, M \qquad \boldsymbol{\mu}, \boldsymbol{M}$ + \subsection{定理环境} + \subsubsection{\LaTeX 原始的定理环境} + \textbackslash newtheorem$\{\langle theorem environment\rangle\}\{\langle title\rangle\}[\langle section-level\rangle]$\\ + \textbackslash newtheorem$\{\langle theorem environment\rangle\}[\langle counter\rangle]\{\langle title\rangle\}$\\ + $\langle theorem environment\rangle$为定理环境的名称。% + $\langle title\rangle$是定理环境的标题(``定理'',``公理''等)。\par + 定理的序号由两个可选参数之一决定,它们不能同时使用: + \renewcommand{\labelitemi}{\textbullet} + \begin{itemize} + \item $\langle section-level\rangle$为章节级别,如 chapter、section 等,% + 定理序号成为章节的下一级序号; + \item $\langle counter\rangle$为用 \textbackslash newcounter 自定义的计数器名称, + 定理序号由这个计数器 管理。 + \end{itemize} + \newtheorem{mythm}{My Theorem}[subsection] + \begin{mythm}\label{thm:light} + The light speed in vacuum% + is $299,792,458\,\mathrm{m/s}$. + \end{mythm} + \begin{mythm}[Energy-momentum relation] + The relationship of energy, % + momentum and mass is% + \[E^2 = m_0^2 c^4 + p^2 c^2\] + where $c$ is the light speed % + described in theorem \ref{thm:light}. + \end{mythm} + \subsubsection{amsthm 宏包} + amsthm 提供了 \textbackslash theoremstyle 命令支持定理格式的切换,% + 在用 \textbackslash newtheorem 命令定义定 理环境之前使用。\\ + amsthm 预定义了三种格式用于 \textbackslash theoremstyle: + \begin{itemize} + \item plain 和 \LaTeX 原始的格式 一致 + \item definition 使用粗体标签、正体内容 + \item remark 使用斜体标签、正体内容 + \end{itemize} + 另外 amsthm 还支持用带星号的 \textbackslash newtheorem* 定义不带序号的定理环境\par + \theoremstyle{definition} \newtheorem{law}{Law} + \theoremstyle{plain} \newtheorem{jury}[law]{Jury} + \theoremstyle{remark} \newtheorem*{mar}{Margaret} + \begin{law}\label{law:box} + Don't hide in the witness box. + \end{law} + \begin{jury}[The Tewlve] + It could be you! So beware and see law~\ref{law:box}. + \end{jury} + \begin{mar} + No, No, No + \end{mar} + \begin{mar} + Denis! + \end{mar} + 以上例子定义的 jury 环境与 law 环境共用编号,mar 环境不编号\par + amsthm 还支持使用 \textbackslash newtheoremstyle 命令自定义定理格式,% + 更为方便使用的是 ntheorem 宏包。 + \subsubsection{证明环境和证毕符号} + amsthm 还提供了一个 proof 环境用于排版定理的证明过程。% + proof 环境末尾自动加上一个 $\Box$ 证毕符号: + \renewcommand{\proofname}{\indent \textit{Proof}} + \begin{proof} + For simplicity, we use + \[ E = mc^2 \] + That's it. + \end{proof} + 如果行末是一个不带编号的公式, 符号会另起一行,% + 这时可使用 \textbackslash qedhere 命令将 号放在公式末尾: + \begin{proof} + For simplicity, we use + \[ E = mc^2 \qedhere \] + \end{proof} + \textbackslash qedhere 对于 align* 等命令也有效: + \begin{proof} + Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then + \begin{align*} + E & = \gamma m_0 c^2 \\ + p & = \gamma m_0 v \qedhere + \end{align*} + \end{proof} + 在使用带编号的公式时,建议最好不要在公式末尾使用 \textbackslash qedhere 命令。% + 对带编号的公式使 用 \textbackslash qedhere 命令会使符号放在一个难看的位置,紧贴着公式: + \begin{proof} + For simplicity, we use + \begin{equation} + E = mc^2 \qedhere + \end{equation} + \end{proof} + \begin{proof} For simplicity, we use + \begin{equation} + E = mc^2 + \end{equation} + \end{proof} + 在 align 等环境中使用 \textbackslash qedhere 命令会使 $\Box$ 盖掉公式的编号: + \begin{proof} + Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then + \begin{align} + E & = \gamma m_0 c^2 \\ + p & = \gamma m_0 v \qedhere + \end{align} + \end{proof} + 使用 equation 嵌套 aligned 等环境时,\textbackslash qedhere 命令会将% + $\Box$ 直接放在公式后: + \begin{proof} + Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then + \begin{equation} + \begin{aligned} + E & = \gamma m_0 c^2 \\ + p & = \gamma m_0 v \qedhere + \end{aligned} + \end{equation} + \end{proof} + 证毕符号 $\Box$ 本身被定义在命令 \textbackslash qedsymbol 中,% + 如果有使用实心符号作为证毕符号的需求, 需要自行用% + \textbackslash renewcommand命令修改 + \renewcommand{\qedsymbol}{\rule{1ex}{1.5ex}} + \renewcommand{\proofname}{\textit{Proof}} + \begin{proof} + For simplicity, we use + \[ E=mc^2 \qedhere \] + \end{proof} \newpage \appendix \section{附录}