update 多行公式 数学符号的字体控制 定理环境
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\usepackage{graphicx}
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\usepackage{subfig}
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\usepackage{amsmath,amsfonts,amssymb,amsthm}
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\usepackage{amsbsy}
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\usepackage{latexsym}
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\usepackage{float}
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\DeclareMathOperator{\argh}{argh}
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\DeclareMathOperator*{\nut}{Nut}
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\usepackage{yhmath}
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\usepackage{eucal,mathrsfs}
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\begin{document}
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\title{标题页}
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@@ -49,6 +52,7 @@
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And I think this is: supercalifragilisticexpialidocious.\par
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\newpage
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\tableofcontents
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\newpage
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\section[目录和页眉页脚]{章节}
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\subsection{子章节}
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\subsubsection{子子章节}
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@@ -561,9 +565,14 @@
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\caption{文本/数学模式通用符号}
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\begin{tabular}{clclclcl}
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\hline
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\{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\
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\{ & \textbackslash\{ & \} & \textbackslash\} & \$ & \textbackslash\$ & \% & \textbackslash\% \\
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\dag & \textbackslash dag & \S & \textbackslash S & \copyright & \textbackslash copyright & \dots & \textbackslash dots \\
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\ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds \\
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\ddag & \textbackslash ddag & \P & \textbackslash P & \pounds & \textbackslash pounds & \S & \textbackslash S \\
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\textasteriskcentered & \textbackslash textasteriskcentered &
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\textperiodcentered & \textbackslash textperiodcentered &
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\textbullet & \textbackslash textbullet \\
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\textregistered{} & \textbackslash textregistered{} &
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\texttrademark & \textbackslash texttrademark \\
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\hline
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\end{tabular}
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\end{table}
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@@ -1050,7 +1059,317 @@
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\bigg\Downarrow \Bigg\Downarrow
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\]
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\subsection{多行公式}
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\subsubsection{长公式折行}
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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 %
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\textbackslash\textbackslash 折行,将 公式编号放在最后一行。%
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多行公式的首行左对齐,末行右对齐,其余行居中。
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\begin{multline}
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a + b + c + d + e + f + g + h + i\\
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= j + k + l + m + n\\
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= o + p + q + r + s\\
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= t + u + v + w + x
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\end{multline}
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类似 equation*,multline* 环境排版不带编号的折行长公式。
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\subsubsection{多行公式}
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罗列一系列公式,并令其按照等号对齐。\\
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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:
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\begin{align}
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a & = b + c \\
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& = d + c
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\end{align}
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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。\\
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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:
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\begin{align}
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a ={} & b + c \\
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={} & d + e + f + g + h + i + j + k + l \notag \\
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& + m + n + o \\
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={} & p + q + r + s
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\end{align}
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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:
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\begin{align}
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a & = 1 & b & = 2 & c & = 3 \\
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d & = - 1 & e & = - 2 & f & = - 5
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\end{align}
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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:
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\begin{gather}
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a = b + c \\
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d = e + f + g \\
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h + i = j + k \\
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l + m = n
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\end{gather}
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align 和 gather 有对应的不带编号的版本 align* 和 gather*
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\subsubsection{公用编号的多行公式}
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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。\\
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amsmath 宏包提供了诸如 aligned、gathered 等环境,%
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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。
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\begin{equation}
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\begin{aligned}
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a & = b + c \\
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d & = e + f + g \\
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h + i & = j + k \\
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l + m & = n
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\end{aligned}
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\end{equation}
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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,
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aligned 允许每行多个公式多栏。
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\subsection{数组和矩阵}
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二维数组,\LaTeX 提供了 array 环境,用法与 tabular 环境极为类似,%
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也需要定 义列格式,并用 \textbackslash \textbackslash 换行。%
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数组可作为一个公式块,在外套用 \textbackslash left、\textbackslash right 等定界符:
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\[
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\mathbf{X} = \left(
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\begin{array}{cccc}
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x_{11} & x_{12} & \ldots & x_{1n} \\
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x_{21} & x_{22} & \ldots & x_{2n} \\
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\vdots & \vdots & \ddots & \vdots \\
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x_{n1} & x_{n2} & \ldots & x_{nn}
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\end{array}
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\right)
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\]
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amsmath 提供的 cases 环境
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\[
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|x| =
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\begin{cases}
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- x & \text{if } x < 0, \\
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0 & \text{if } x = 0, \\
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x & \text{if } x > 0.
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\end{cases}
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\]
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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 ($\left(\right.$) 、
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bmatrix ($\left[\right.$) 、 Bmatrix ($\left\{\right.$) 。使用这些环境时,无需给定列格式 :
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\[
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\begin{matrix}
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1 & 2 \\
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3 & 4
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\end{matrix} \qquad
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\begin{bmatrix}
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x_{11} & x_{12} & \ldots & x_{1n} \\
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x_{21} & x_{22} & \ldots & x_{2n} \\
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\vdots & \vdots & \ddots & \vdots \\
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x_{n1} & x_{n2} & \ldots & x_{nn}
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\end{bmatrix}
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\]
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在矩阵中的元素里排版分式时,一来要用到 \textbackslash dfrac 等命令,%
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二来行与行之间有可能紧贴着, 这时要调节间距:
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\[
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\mathbf{H} =
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\begin{bmatrix}
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\dfrac{\partial^2 f}{\partial x^2} & \dfrac{\partial^2 f}{\partial x\partial y} \\[8pt]
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\dfrac{\partial^2 f}{\partial x\partial y} & \dfrac{\partial^2 f}{\partial y^2}
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\end{bmatrix}
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\]
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\subsection{公式中的间距}
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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\\
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\textbackslash ,、\textbackslash :、\textbackslash ; 以及负间距 \textbackslash ! %
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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
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\begin{table}[H]
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\centering
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\begin{tabular}{ll|ll}
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\hline
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无额外间距 & aa &
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\textbackslash , & a\,a \\
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\textbackslash quad & a\quad a &
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\textbackslash : & a\:a \\
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\textbackslash qquad & a\qquad a &
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\textbackslash ; & a\;a \\
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\textbackslash \verb*| | & a\ a &
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\textbackslash ! & a\!a \\
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\hline
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\end{tabular}
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\end{table}
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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。
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\[
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\int_a^b f(x) \mathrm{d}x
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\qquad
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\int_a^b f(x) \, \mathrm{d}x
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\]
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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,%
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之间的间距将会过宽,此时 可以使用负间距 \textbackslash ! 修正之。
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\begin{gather*}
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\int\int f(x)g(y) \,\mathrm{d}x\,\mathrm{d}y \\
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\int\!\!\!\int f(x)g(y) \mathrm{d}\,x\mathrm{d}\,y
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\end{gather*}
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amsmath 提供了更方便的多重积分号,如二重积分 \textbackslash iint、%
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三 重积分 \textbackslash iiint 等。
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\begin{gather*}
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\iint f(x)g(y) \,\mathrm{d}x\,\mathrm{d}y \\
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\iint \quad \iiint \quad \idotsint
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\end{gather*}
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\subsection{数学符号的字体控制}
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\subsubsection{数学字母字体}
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\begin{table}[H]
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\centering
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\caption{数学字母字体}
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\begin{tabular}{lll}
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\toprule
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示例 &命令 &依赖的宏包\\
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\midrule
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$\mathnormal{ABCDEabcde1234}$ & \textbackslash mathnormal\{\ldots\} & \\
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$\mathrm{ABCDEabcde1234}$ & \textbackslash mathrm\{\ldots\} & \\
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$\mathit{ABCDEabcde1234}$ & \textbackslash mathit\{\ldots\} & \\
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$\mathbf{ABCDEabcde1234}$ & \textbackslash mathbf\{\ldots\} & \\
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$\mathsf{ABCDEabcde1234}$ & \textbackslash mathsf\{\ldots\} & \\
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$\mathtt{ABCDEabcde1234}$ & \textbackslash mathtt\{\ldots\} & \\
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$\mathcal{ABCDEabcde1234}$ & \textbackslash mathcal\{\ldots\} & 只大写字母 \\
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\midrule
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$\mathcal{ABCDE}$ & \textbackslash mathcal\{\ldots\} & eucal,只大写字母 \\
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$\mathscr{ABCDE}$ & \textbackslash mathscr\{\ldots\} & mathrsfs,只大写字母 \\
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$\mathfrak{ABCDEabcde1234}$ & \textbackslash mathfrak\{\ldots\} & amssymb 或 eufrak \\
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$\mathbb{ABCDE}$ & \textbackslash mathbb\{\ldots\} & amssymb,只大写字母 \\
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\bottomrule
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\end{tabular}
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\end{table}
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\[ \mathcal{R} \quad \mathfrak{R \quad \mathbb{R}} \]
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\[ \mathcal{L} = -\frac{1}{4}F_{\mu\nu}F^{\mu\nu} \]
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$\mathfrak{su}(2)$ and $\mathfrak{so}(3)$ Lie algebra
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\subsubsection{数学符号的尺寸}
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\begin{table}[H]
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\centering
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\caption{数学符号尺寸}
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\begin{tabular}{lll}
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\toprule
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命令 &尺寸 &示例\\
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\midrule
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\textbackslash displaystyle & 行间公式尺寸 & $\displaystyle \sum a$ \\
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\textbackslash textstyle & 行内公式尺寸 & $\textstyle \sum a$ \\
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\textbackslash scriptstyle & 上下标尺寸 & $\scriptstyle a$ \\
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\textbackslash scriptscriptstyle & 次级上下标尺寸 & $\scriptscriptstyle a$ \\
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\bottomrule
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\end{tabular}
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\end{table}
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\[
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P = \frac
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{\sum_{i = 1}^n (x_i - x)(y_i - y)}
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{\displaystyle \left[
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\sum_{i = 1}^n (x_i - x)^2
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\sum_{i = 1}^n (y_i - y)^2
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\right]^{1/2}}\,
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\]
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\subsubsection{加粗的数学符号}
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\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
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$\mu, M \qquad \mathbf{\mu}, \mathbf{M}$ \qquad
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{\boldmath$\mu, M$\par}
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amsmath 提供了一个 \textbackslash boldsymbol 命令(由调用的 amsbsy 宏包提供) ,%
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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
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$\mu, M \qquad \boldsymbol{\mu}, \boldsymbol{M}$
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\subsection{定理环境}
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\subsubsection{\LaTeX 原始的定理环境}
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\textbackslash newtheorem$\{\langle theorem environment\rangle\}\{\langle title\rangle\}[\langle section-level\rangle]$\\
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\textbackslash newtheorem$\{\langle theorem environment\rangle\}[\langle counter\rangle]\{\langle title\rangle\}$\\
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$\langle theorem environment\rangle$为定理环境的名称。%
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$\langle title\rangle$是定理环境的标题(``定理'',``公理''等)。\par
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定理的序号由两个可选参数之一决定,它们不能同时使用:
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\renewcommand{\labelitemi}{\textbullet}
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\begin{itemize}
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\item $\langle section-level\rangle$为章节级别,如 chapter、section 等,%
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定理序号成为章节的下一级序号;
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\item $\langle counter\rangle$为用 \textbackslash newcounter 自定义的计数器名称,
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定理序号由这个计数器 管理。
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\end{itemize}
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\newtheorem{mythm}{My Theorem}[subsection]
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\begin{mythm}\label{thm:light}
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The light speed in vacuum%
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is $299,792,458\,\mathrm{m/s}$.
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\end{mythm}
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\begin{mythm}[Energy-momentum relation]
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The relationship of energy, %
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momentum and mass is%
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\[E^2 = m_0^2 c^4 + p^2 c^2\]
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where $c$ is the light speed %
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described in theorem \ref{thm:light}.
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\end{mythm}
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\subsubsection{amsthm 宏包}
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amsthm 提供了 \textbackslash theoremstyle 命令支持定理格式的切换,%
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在用 \textbackslash newtheorem 命令定义定 理环境之前使用。\\
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amsthm 预定义了三种格式用于 \textbackslash theoremstyle:
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\begin{itemize}
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\item plain 和 \LaTeX 原始的格式 一致
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\item definition 使用粗体标签、正体内容
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\item remark 使用斜体标签、正体内容
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\end{itemize}
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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
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\theoremstyle{definition} \newtheorem{law}{Law}
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\theoremstyle{plain} \newtheorem{jury}[law]{Jury}
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\theoremstyle{remark} \newtheorem*{mar}{Margaret}
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\begin{law}\label{law:box}
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Don't hide in the witness box.
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\end{law}
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\begin{jury}[The Tewlve]
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It could be you! So beware and see law~\ref{law:box}.
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\end{jury}
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\begin{mar}
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No, No, No
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\end{mar}
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\begin{mar}
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Denis!
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\end{mar}
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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
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amsthm 还支持使用 \textbackslash newtheoremstyle 命令自定义定理格式,%
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更为方便使用的是 ntheorem 宏包。
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\subsubsection{证明环境和证毕符号}
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amsthm 还提供了一个 proof 环境用于排版定理的证明过程。%
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proof 环境末尾自动加上一个 $\Box$ 证毕符号:
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\renewcommand{\proofname}{\indent \textit{Proof}}
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\begin{proof}
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For simplicity, we use
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\[ E = mc^2 \]
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That's it.
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\end{proof}
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如果行末是一个不带编号的公式, 符号会另起一行,%
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这时可使用 \textbackslash qedhere 命令将 号放在公式末尾:
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\begin{proof}
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For simplicity, we use
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\[ E = mc^2 \qedhere \]
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\end{proof}
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\textbackslash qedhere 对于 align* 等命令也有效:
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\begin{proof}
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Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then
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\begin{align*}
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E & = \gamma m_0 c^2 \\
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p & = \gamma m_0 v \qedhere
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\end{align*}
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\end{proof}
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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。%
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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:
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\begin{proof}
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For simplicity, we use
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\begin{equation}
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E = mc^2 \qedhere
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\end{equation}
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\end{proof}
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\begin{proof} For simplicity, we use
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\begin{equation}
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E = mc^2
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\end{equation}
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\end{proof}
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在 align 等环境中使用 \textbackslash qedhere 命令会使 $\Box$ 盖掉公式的编号:
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\begin{proof}
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Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then
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\begin{align}
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E & = \gamma m_0 c^2 \\
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p & = \gamma m_0 v \qedhere
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\end{align}
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\end{proof}
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使用 equation 嵌套 aligned 等环境时,\textbackslash qedhere 命令会将%
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$\Box$ 直接放在公式后:
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\begin{proof}
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Assuming $\gamma = 1/\sqrt{a-v^2/c^2}$, then
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\begin{equation}
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\begin{aligned}
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E & = \gamma m_0 c^2 \\
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p & = \gamma m_0 v \qedhere
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\end{aligned}
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\end{equation}
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\end{proof}
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证毕符号 $\Box$ 本身被定义在命令 \textbackslash qedsymbol 中,%
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如果有使用实心符号作为证毕符号的需求, 需要自行用%
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\textbackslash renewcommand命令修改
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\renewcommand{\qedsymbol}{\rule{1ex}{1.5ex}}
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\renewcommand{\proofname}{\textit{Proof}}
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\begin{proof}
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||||
For simplicity, we use
|
||||
\[ E=mc^2 \qedhere \]
|
||||
\end{proof}
|
||||
\newpage
|
||||
\appendix
|
||||
\section{附录}
|
||||
|
||||
Reference in New Issue
Block a user