Latex(数学）

为美赛做个准备吧，正好把latex一些用法整理一下。
以tex live为准。

字体

罗马字体 \mathrm{}

for i in range(97, 123):
    print('$\\mathrm{{{0}}}$'.format(chr(i)))

$\mathrm{*}$

for i in range(65, 91):
    print('$\\mathrm{{{0}}}$'.format(chr(i)))

$\mathrm{*}$

斜体 \mathit{}

$\mathit{*}$

for i in range(97, 123):
    print('$\\mathit{{{0}}}$'.format(chr(i)))

for i in range(65, 91):
    print('$\\mathit{{{0}}}$'.format(chr(i)))

粗体 \mathbf{}

$\mathbf{*}$

for i in range(97, 123):
    print('$\\mathbf{{{0}}}$'.format(chr(i)))

for i in range(65, 91):
    print('$\\mathbf{{{0}}}$'.format(chr(i)))

无衬线-f \mathsf{}

$\mathsf{*}$

for i in range(97, 123):
    print('$\\mathsf{{{0}}}$'.format(chr(i)))

for i in range(65, 91):
    print('$\\mathsf{{{0}}}$'.format(chr(i)))

打字机字体 \mathtt{}

$\mathtt{*}$

for i in range(97, 123):
    print('$\\mathtt{{{0}}}$'.format(chr(i)))

for i in range(65, 91):
    print('$\\mathtt{{{0}}}$'.format(chr(i)))

书法字体 \mathcal{}

$\mathcal{*}$

for i in range(65, 91):
    print('$\\mathcal{{{0}}}$'.format(chr(i)))

注:小写字母貌似没有

黑板粗体 \mathbb{} \usepackage{amssymb}

$\mathbb{*}$

for i in range(65, 91):
    print('$\\mathbb{{{0}}}$'.format(chr(i)))

注: 小写字母貌似没有

德文尖角体 \mathfrak{} \usepackage{amssymb}

$\mathfrak{*}$

for i in range(97, 123):
    print('$\\mathfrak{{{0}}}$'.format(chr(i)))

for i in range(65, 91):
    print('$\\mathfrak{{{0}}}$'.format(chr(i)))

花体 \mathscr{} \usepackage{mathrsfs}

$\mathscr{}$

for i in range(65, 91):
    print('$\\mathscr{{{0}}}$'.format(chr(i)))

注:小写貌似没有

数学符号表（摘自《140分钟学会LaTex》）

数学模式重音符号（头顶上的那玩意）

希腊字母

二元关系

$\not\in$

\(\not\in\)

二元运算符

“大”运算符

箭头

定界符

大定界符

其他符号(AMS的符号就不贴了)

一些数学公式写法的例子

$\mathbf{Var}[(CR)_{ij}] = \mathop{\sum}\limits_{t=1}^{c}\mathbf{Var}[X_t]
=\mathop{\sum}\limits_{k=1}^{n}\frac{A_{ik}^{2}B_{kj}^{2}}{cp_k}
-\frac{1}{c}(AB)_{ij}^2$

\(\mathbf{Var}[(CR)_{ij}] = \mathop{\sum}\limits_{t=1}^{c}\mathbf{Var}[X_t] =\mathop{\sum}\limits_{k=1}^{n}\frac{A_{ik}^{2}B_{kj}^{2}}{cp_k} -\frac{1}{c}(AB)_{ij}^2\)

\begin{displaymath}
    \begin{array}{ll}
        \min & E[\|AB-CR\|_F^2]\\
        s.t. & \mathop{\sum}\limits_{i=1}^{n}p_i = 1
    \end{array}
\end{displaymath}

\[ \begin{array}{ll} \min & E[\|AB-CR\|_F^2]\\ s.t. & \mathop{\sum}\limits_{i=1}^{n}p_i = 1 \end{array} \]

\[ #\usepackage{amssymb, amsmath}
\begin{split}
x_k = & x_{k-1} + \gamma_k[A_kx_{k-1}-(x_{k-1}^{\top}A_kx_{k-1})x_{k-1}]\\
=& x_{k-1} + \gamma_k[Ax_{k-1}-(x_{k-1}^{\mathrm{T}}Ax_{k-1})x_{k-1}]\\
&+\gamma_k[(A_k-A)x_{k-1}-(x_{k-1}^{\top}(A_k-A)x_{k-1})x_{k-1}
\end{split}
\]

\begin{equation} \label{eq:1}
    \frac{\mathrm{d}\|z\|_2^{2}}{\mathrm{d}t} = 2z\frac{\mathrm{d}z}{\mathrm{d}t} = 0
\end{equation}
#\ref{eq:1}引用

$\underbrace{a+b+\cdots+z}_{26}$

\(\underbrace{a+b+\cdots+z}_{26}\)

\begin{displaymath} 
\mathbf{X} =
\left( \begin{array}{ccc} 
x_{11} & x_{12} & \ldots \\ 
x_{21} & x_{22} & \ldots \\ 
 \vdots & \vdots & \ddots 
\end{array} \right) 
\end{displaymath}

\begin{displaymath} 
y = \left\{ \begin{array}{ll} 
a & \textrm{if $d>c$}\\ 
b+x & \textrm{in the morning}\\ 
l & \textrm{all day long} 
\end{array} \right. 
\end{displaymath}

\[ y = \left\{ \begin{array}{ll} a & \textrm{if $d>c$}\\ b+x & \textrm{in the morning}\\ l & \textrm{all day long} \end{array} \right. \]

\begin{displaymath} 
\left(\begin{array}{c|c} 
1 & 2 \\ 
\hline 
3 & 4 
\end{array}\right) 
\end{displaymath}

\[ \left(\begin{array}{c|c} 1 & 2 \\ \hline 3 & 4 \end{array}\right) \]

\begin{displaymath} 
{}^{12}_{\phantom{1}6}\textrm{C} 
\qquad \textrm{versus} \qquad 
{}^{12}_{6}\textrm{C} 
\end{displaymath}

\[ {}^{12}_{\phantom{1}6}\textrm{C} \qquad \textrm{versus} \qquad {}^{12}_{6}\textrm{C} \]

\begin{displaymath}
\frac{\mathrm{d}f}{\mathrm{d}\theta}=
\mathrm{(\cos \theta, -\sin \theta)}
\left(\begin{array}{cc}
    \mathrm{x_1^T}\\
    \mathrm{x_2^T}
\end{array} \right)
\mathrm{A}
\mathrm{(x_1, x_2)}
\left(\begin{array}{cc}
\sin \theta\\
\cos \theta
\end{array} \right)
\end{displaymath}