矩阵 | Matrices
\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix}
\begin{pmatrix}1&2\\3&4\\ \end{pmatrix}
\begin{bmatrix}1&2\\3&4\\ \end{bmatrix}
\begin{Bmatrix}1&2\\3&4\\ \end{Bmatrix}
\begin{vmatrix}1&2\\3&4\\ \end{vmatrix}
\begin{Vmatrix}1&2\\3&4\\ \end{Vmatrix}
\begin{pmatrix} 1 & a_1 & a_1^2 & \cdots & a_1^n \\ 1 & a_2 & a_2^2 & \cdots & a_2^n \\ \vdots & \vdots& \vdots & \ddots & \vdots \\ 1 & a_m & a_m^2 & \cdots & a_m^n \end{pmatrix}
\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right]
\begin{pmatrix} a & b\\ c & d\\ \hline 1 & 0\\ 0 & 1 \end{pmatrix}
$\bigl( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \bigr)$对齐方程 | Aligned equations
\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align}
\begin{align} f(x)&=\left(x^3\right)+\left(x^3+x^2+x^1\right)+\left(x^3+x^2\right)\\ f'(x)&=\left(3x^2+2x+1\right)+\left(3x^2+2x\right)\\ f''(x)&=\left(6x+2\right)\\ \end{align}分段函数 | piecewise functions
f(n) = \begin{cases} n/2, & \text{if $n$ is even} \\ 3n+1, & \text{if $n$ is odd} \end{cases}
\left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n)
f(n) = \begin{cases} \frac{n}{2}, & \text{if $n$ is even} \\[2ex] 3n+1, & \text{if $n$ is odd} \end{cases}
数组 | Arrays
\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array}
% outer vertical array of arrays \begin{array}{c} % inner horizontal array of arrays \begin{array}{cc} % inner array of minimum values \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & % inner array of maximum values \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} \\ % inner array of delta values \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} \end{array}
\begin{array}{ll} \hfill\mathrm{Bad}\hfill & \hfill\mathrm{Better}\hfill \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array}方程组 | System of equations
\left\{ \begin{array}{c} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{array} \right.
\begin{cases} a_1x+b_1y+c_1z=d_1 \\ a_2x+b_2y+c_2z=d_2 \\ a_3x+b_3y+c_3z=d_3 \end{cases}
\left\{ \begin{aligned} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y&=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{aligned} \right.
\left\{ \begin{array}{ll} a_1x+b_1y+c_1z &=d_1+e_1 \\ a_2x+b_2y &=d_2 \\ a_3x+b_3y+c_3z &=d_3 \end{array} \right.
\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\[2ex] a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\[2ex] a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}
\begin{cases} a_1x+b_1y+c_1z=\frac{p_1}{q_1} \\ a_2x+b_2y+c_2z=\frac{p_2}{q_2} \\ a_3x+b_3y+c_3z=\frac{p_3}{q_3} \end{cases}
\left\{ \begin{array}{l} 0 = c_x-a_{x0}-d_{x0}\dfrac{(c_x-a_{x0})\cdot d_{x0}}{\|d_{x0}\|^2} + c_x-a_{x1}-d_{x1}\dfrac{(c_x-a_{x1})\cdot d_{x1}}{\|d_{x1}\|^2} \\[2ex] 0 = c_y-a_{y0}-d_{y0}\dfrac{(c_y-a_{y0})\cdot d_{y0}}{\|d_{y0}\|^2} + c_y-a_{y1}-d_{y1}\dfrac{(c_y-a_{y1})\cdot d_{y1}}{\|d_{y1}\|^2} \end{array} \right.
颜色 | Colors
\begin{array}{|rc|} \hline \verb+\color{black}{text}+ & \color{black}{text} \\ \verb+\color{gray}{text}+ & \color{gray}{text} \\ \verb+\color{silver}{text}+ & \color{silver}{text} \\ \verb+\color{white}{text}+ & \color{white}{text} \\ \hline \verb+\color{maroon}{text}+ & \color{maroon}{text} \\ \verb+\color{red}{text}+ & \color{red}{text} \\ \verb+\color{yellow}{text}+ & \color{yellow}{text} \\ \verb+\color{lime}{text}+ & \color{lime}{text} \\ \verb+\color{olive}{text}+ & \color{olive}{text} \\ \verb+\color{green}{text}+ & \color{green}{text} \\ \verb+\color{teal}{text}+ & \color{teal}{text} \\ \verb+\color{aqua}{text}+ & \color{aqua}{text} \\ \verb+\color{blue}{text}+ & \color{blue}{text} \\ \verb+\color{navy}{text}+ & \color{navy}{text} \\ \verb+\color{purple}{text}+ & \color{purple}{text} \\ \verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\ \hline \end{array}
\begin{array}{|rc|} \hline \verb+\color{black}{text}+ & \color{black}{text} \\ \verb+\color{gray}{text}+ & \color{gray}{text} \\ \verb+\color{silver}{text}+ & \color{silver}{text} \\ \verb+\color{white}{text}+ & \color{white}{text} \\ \hline \verb+\color{maroon}{text}+ & \color{maroon}{text} \\ \verb+\color{red}{text}+ & \color{red}{text} \\ \verb+\color{yellow}{text}+ & \color{yellow}{text} \\ \verb+\color{lime}{text}+ & \color{lime}{text} \\ \verb+\color{olive}{text}+ & \color{olive}{text} \\ \verb+\color{green}{text}+ & \color{green}{text} \\ \verb+\color{teal}{text}+ & \color{teal}{text} \\ \verb+\color{aqua}{text}+ & \color{aqua}{text} \\ \verb+\color{blue}{text}+ & \color{blue}{text} \\ \verb+\color{navy}{text}+ & \color{navy}{text} \\ \verb+\color{purple}{text}+ & \color{purple}{text} \\ \verb+\color{fuchsia}{text}+ & \color{magenta}{text} \\ \hline \end{array}
交换图 | Commutative diagrams
\begin{CD} A @>a>> B\\ @V b V V= @VV c V\\ C @>>d> D \end{CD}
\begin{CD} A @>>> B @>{\text{very long label}}>> C \\ @. @AAA @| \\ D @= E @<<< F \end{CD}
\begin{CD} RCOHR'SO_3Na @>{\text{Hydrolysis,$\Delta, Dil.HCl$}}>> (RCOR')+NaCl+SO_2+ H_2O \end{CD}
持续分数 | Continued fractions
x = a_0 + \cfrac{1^2}{a_1 + \cfrac{2^2}{a_2 + \cfrac{3^2}{a_3 + \cfrac{4^4}{a_4 + \cdots}}}}
x = a_0 + \frac{1^2}{a_1 + \frac{2^2}{a_2 + \frac{3^2}{a_3 + \frac{4^4}{a_4 + \cdots}}}}
x = a_0 + \frac{1^2}{a_1+} \frac{2^2}{a_2+} \frac{3^2}{a_3 +} \frac{4^4}{a_4 +} \cdots
\cfrac{a_{1}}{b_{1}+\cfrac{a_{2}}{b_{2}+\cfrac{a_{3}}{b_{3}+\ddots }}}= {\genfrac{}{}{}{}{a_1}{b_1}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_2}{b_2}} {\genfrac{}{}{0pt}{}{}{+}} {\genfrac{}{}{}{}{a_3}{b_3}} {\genfrac{}{}{0pt}{}{}{+\dots}}
\underset{j=1}{\overset{\infty}{\LARGE\mathrm K}}\frac{a_j}{b_j}=\cfrac{a_1}{b_1+\cfrac{a_2}{b_2+\cfrac{a_3}{b_3+\ddots}}}.
\mathop{\LARGE\mathrm K}_{i=1}^\infty \frac{a_i}{b_i}大括号 | Big braces
f\left( \left[ \frac{ 1+\left\{x,y\right\} }{ \left( \frac{x}{y}+\frac{y}{x} \right) \left(u+1\right) }+a \right]^{3/2} \right)
\begin{aligned} a=&\left(1+2+3+ \cdots \right. \\ & \cdots+ \left. \infty-2+\infty-1+\infty\right) \end{aligned}
\left\langle q \middle\| \frac{\frac{x}{y}}{\frac{u}{v}} \middle| p \right\rangle
高亮 | Highlighting equation
\bbox[yellow] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1) }
\bbox[yellow,5px] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1) }
\bbox[5px,border:2px solid red] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (2) }
\bbox[yellow,5px,border:2px solid red] { e^x=\lim_{n\to\infty} \left( 1+\frac{x}{n} \right)^n \qquad (1) }
Pack of cards
\spadesuit\quad\heartsuit\quad\diamondsuit\quad\clubsuit\color{red}{\heartsuit}\quad\color{red}{\diamondsuit}
♠\quad♡\quad♢\quad♣\\ ♤\quad♥\quad♦\quad♧
长除法 | Long division
\require{enclose} \begin{array}{r} 13 \\[-3pt] 4 \enclose{longdiv}{52} \\[-3pt] \underline{4}\phantom{2} \\[-3pt] 12 \\[-3pt] \underline{12} \end{array}
\begin{array}{c|rrrr}& x^3 & x^2 & x^1 & x^0\\ & 1 & -6 & 11 & -6\\ {\color{red}1} & \downarrow & 1 & -5 & 6\\ \hline & 1 & -5 & 6 & |\phantom{-} {\color{blue}0} \end{array}
x^3−6x^2+11x−6=(x−{\color{red}1})(x^2−5x+6)+{\color{blue}0}Degree symbol
\begin{array} \\ \text{45^\text{o}} & \text{renders as} & 45^\text{o} \\ \text{45^o} & \text{renders as} & 45^o \\ \text{45^\circ} & \text{renders as} & 45^\circ \\ \text{90°} & \text{renders as} & 90° & \text{Using keyboard entry of symbol} % % Use the following line as a template for additional entries % % \text{} & \text{renders as} & \\ \end{array}
其他 | Others
\sum_{n=1}^\infty \frac{1}{n^2} \to \textstyle \sum_{n=1}^\infty \frac{1}{n^2} \to \displaystyle \sum_{n=1}^\infty \frac{1}{n^2}
Compare 
versus 
能量守恒
e=mc^2 \tag{1}\label{eq1}
\begin{equation}\begin{aligned} a &= b + c \\ &= d + e + f + g \\ &= h + i \end{aligned}\end{equation}\tag{2}\label{eq2}
\begin{align} a &= b + c \tag{3}\label{eq3} \\ x &= yz \tag{4}\label{eq4}\\ l &= m - n \tag{5}\label{eq5} \end{align}
54\,321.123\,45
\left.\mathrm{m}\middle/\mathrm{s}^2\right.
\mu_0=4\pi\times10^{-7} \ \left.\mathrm{\mathrm{T}\!\cdot\!\mathrm{m}}\middle/\mathrm{A}\right.
\begin{array}{rrrrrr|r} & x_1 & x_2 & s_1 & s_2 & s_3 & \\ \hline s_1 & 0 & 1 & 1 & 0 & 0 & 8 \\ s_2 & 1 & -1 & 0 & 1 & 0 & 4 \\ s_3 & 1 & 1 & 0 & 0 & 1 & 12 \\ \hline & -1 & -1 & 0 & 0 & 0 & 0 \end{array}
\begin{array}{rrrrrrr|rr} & x_1 & x_2 & s_1 & s_2 & s_3 & w & & \text{ratio} \\ \hline s_1 & 0 & 1 & 1 & 0 & 0 & 0 & 8 & - \\ w & 1^* & -1 & 0 & -1 & 0 & 1 & 4 & 4 \\ s_3 & 1 & 1 & 0 & 0 & 1 & 0 & 12 & 12 \\ \hdashline & 1 & -1 & 0 & -1 & 0 & 0 & 4 & \\ \hline s_1 & 0 & 1 & 1 & 0 & 0 & 0 & 8 & \\ x_1 & 1 & -1 & 0 & -1 & 0 & 1 & 4 & \\ s_3 & 0 & 2 & 0 & 2 & 1 & -1 & 8 & \\ \hdashline & 0 & 0 & 0 & 0 & 0 & -1 & 0 & \end{array}
\begin{array}{rrrrrrrr|r} & x_1 & x_2 & x_3 & x_4 & x_5 & x_6 & x_7 & \\ \hline x_4 & 0 & -3 & 7 & 1 & 0 & 0 & 2 & 2M -4 \\ x_5 & 0 & -9 & 0 & 0 & 1 & 0 & -1 & -M -3 \\ x_6 & 0 & 6 & -1 & 0 & 0 & 1 & -4^* & -4M +8 \\ x_1 & 1 & 0 & 1 & 0 & 0 & 0 & 1 & M \\ \hline & 0 & 1 & 1 & 0 & 0 & 0 & 2 & 2M \\ \text{ratio} & & & 1 & & & & 1/2 & \end{array}
\begin{array}{rrrrrrr|r} & x_1 & x_2 & x_3 & s_1 & s_2 & s_3 & \\ \hline s_1 & -2 & 0 & -2 & 1 & 0 & 0 & -60 \\ s_2 & -2 & -4^* & -5 & 0 & 1 & 0 & -70 \\ s_3 & 0 & -3 & -1 & 0 & 0 & 1 & -27 \\ \hdashline & 8 & 10 & 25 & 0 & 0 & 0 & 0 \\ \text{ratio} & -4 & -5/2 & -5 & & & & \\ \hline s_1 & -2^* & 0 & -2 & 1 & 0 & 0 & -60 \\ x_2 & 1/2 & 1 & 5/4 & 0 & -1/4 & 0 & 35/2 \\ s_3 & 3/2 & 0 & 11/4 & 0 & -3/4 & 1 & 51/2 \\ \hdashline & 3 & 0 & 25/2 & 0 & 5/2 & 0 & -175 \\ \text{ratio} & -3/2 & & 25/4 & & & & \\ \hline x_1 & 1 & 0 & 1 & -1/2 & 0 & 0 & 30 \\ x_2 & 0 & 1 & 3/4 & 1/4 & -1/4 & 0 & 5/2 \\ s_3 & 0 & 0 & 5/4 & 3/4 & -3/4^* & 1 & -39/2 \\ \hdashline & 0 & 0 & 19/2 & 3/2 & 5/2 & 0 & -265 \\ \text{ratio} & & & & & \dots & & \\ \hline x_1 & 1 & 0 & 1 & -1/2 & 0 & 0 & 30 \\ x_2 & 0 & 1 & 1/3 & 0 & 0 & -1/3 & 9 \\ s_2 & 0 & 0 & -5/3 & -1 & 1 & -4/3 & 26 \\ \hdashline & 0 & 0 & 41/3 & 4 & 0 & 10/3 & -330 \end{array}
\require{extpfeil} % produce extensible horizontal arrows \begin{array}{ccc} % arrange LPPs % first row % first LPP \begin{array}{ll} \max & z = c^T x \\ \text{s.t.} & A x \le b \\ & x \ge 0 \end{array} & \xtofrom{\text{duality}} & % second LPP \begin{array}{ll} \min & v = b^T y \\ \text{s.t.} & A^T y \ge c \\ & y \ge 0 \end{array} \\ ({\cal PC}) & & ({\cal DC}) \\ \text{add } {\Large \downharpoonleft} \text{slack var} & & \text{minus } {\Large \downharpoonright} \text{surplus var}\\ % Change to your favorite arrow style % % second row % third LPP \begin{array}{ll} \max & z = c^T x \\ \text{s.t.} & A x + s = b \\ & x,s \ge 0 \end{array} & \xtofrom[\text{some steps skipped}]{\text{duality}} & % fourth LPP \begin{array}{ll} \min & v = b^T y \\ \text{s.t.} & A^T y - t = c \\ & y,t \ge 0 \end{array} \\ ({\cal PS}) & & ({\cal DS}) % \end{array}
\Large\LaTeX
\sum_{i=0}^n i^2 = \frac{(n^2+n)(2n+1)}{6}
\Biggl(\biggl(\Bigl(\bigl((egg)\bigr)\Bigr)\biggr)\Biggr)字体 | Fonts
\mathbb{CHNQRZ}
\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\mathbf{abcdefghijklmnopqrstuvwxyz}
\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}
\mathit{abcdefghijklmnopqrstuvwxyz}
\pmb{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathtt{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ,abcdefghijklmnopqrstuvwxyz}
\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ} \mathfrak{abcdefghijklmnopqrstuvwxyz}