标准函数
| \exp_a b = a^b, \exp b = e^b, 10^m |
$\exp_a$ b = a^b$, $\exp b = e^b$, $10^m$ |
| \ln c, \lg d = \log e, \log_{10} f |
$\ln c$, $\lg d = \log e$, $\log_{10} f$ |
| \sin a, \cos b, \tan c, \cot d, \sec e, \csc f |
$\sin a$, $\cos b$, $\tan c$, $\cot d$, $\sec e$, $\csc f$ |
| \arcsin a, \arccos b, \arctan c |
$\arcsin a$, $\arccos b$, $\arctan c$ |
| \arccot d, \arcsec e, \arccsc f |
$\arccot d$, $\arcsec e$, $\arccsc f$ |
| \sinh a, \cosh b, \tanh c, \coth d |
$\sinh a$, $\cosh b$, $\tanh c$, $\coth d$ |
| \operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n |
$\operatorname{sh}k$, $\operatorname{ch}l$, $\operatorname{th}m$, $\operatorname{coth}n$ |
| \operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q |
$\operatorname{argsh}o$, $\operatorname{argch}p$, $\operatorname{argth}q$ |
| \sgn r, \left\vert s \right\vert |
$\sgn r$, $\left\vert s \right\vert$ |
| \min(x,y), \max(x,y) |
$\min(x,y)$, $\max(x,y)$ |
运算符
| +, -, \pm, \mp, \dotplus |
$+$, $-$, $\pm$, $\mp$, $\dotplus$ |
| \times, \div, \divideontimes, /, \backslash |
$\times$, $\div$, $\divideontimes$, $/$, $\backslash$ |
| \cdot, * \ast, \star, \circ, \bullet |
$\cdot$, $* \ast$, $\star$, $\circ$, $\bullet$ |
| \boxplus, \boxminus, \boxtimes, \boxdot |
$\boxplus$, $\boxminus$, $\boxtimes$, $\boxdot$ |
| \oplus, \ominus, \otimes, \oslash, \odot |
$\oplus$, $\ominus$, $\otimes$, $\oslash$, $\odot$ |
| \circleddash, \circledcirc, \circledast |
$\circleddash$, $\circledcirc$, $\circledast$ |
| \bigoplus, \bigotimes, \bigodot |
$\bigoplus$, $\bigotimes$, $\bigodot$ |
集合
| \{ \}, \O \empty \emptyset, \varnothing |
$\{ \}$, $\O \empty \emptyset$, $\varnothing$ |
| \in, \notin \not\in, \ni, \not\ni |
$\in$, $\notin \not\in$, $\ni$, $\not\ni$ |
| \cap, \Cap, \sqcap, \bigcap |
$\cap$, $\Cap$, $\sqcap$, $\bigcap$ |
| \cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus |
$\cup$, $\Cup$, $\sqcup$, $\bigcup$, $\bigsqcup$, $\uplus$, $\biguplus$ |
| \setminus, \smallsetminus, \times |
$\setminus$, $\smallsetminus$, $\times$ |
| \subset, \Subset, \sqsubset |
$\subset$, $\Subset$, $\sqsubset$ |
| \supset, \Supset, \sqsupset |
$\supset$, $\Supset$, $\sqsupset$ |
| \subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq |
$\subseteq$, $\nsubseteq$, $\subsetneq$, $\varsubsetneq$, $\sqsubseteq$ |
| \supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq |
$\supseteq$, $\nsupseteq$, $\supsetneq$, $\varsupsetneq$, $\sqsupseteq$ |
| \subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq |
$\subseteqq$, $\nsubseteqq$, $\subsetneqq$, $\varsubsetneqq$ |
| \supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq |
$\supseteqq$, $\nsupseteqq$, $\supsetneqq$, $\varsupsetneqq$ |
关系符号
| =, \ne, \neq, \equiv, \not\equiv |
$=$, $\ne$, $\neq$, $\equiv$, $\not\equiv$ |
| \doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, := |
$\doteq$, $\doteqdot$, $\overset{\underset{\mathrm{def}}{}}{=}$, $:=$ |
| \sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong |
$\sim$, $\nsim$, $\backsim$, $\thicksim$, $\simeq$, $\backsimeq$, $\eqsim$, $\cong$, $\ncong$ |
| \approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto |
$\approx$, $\thickapprox$, $\approxeq$, $\asymp$, $\propto$, $\varpropto$ |
| $<$,\nless, \ll, \not\ll, \lll, \not\lll, \lessdot |
$<$, $\nless$, $\ll$, $\not\ll$, $\lll$, $\not\lll$, $\lessdot$ |
| >, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot |
$>$, $\ngtr$, $\gg$, $\not\gg$, $\ggg$, $\not\ggg$, $\gtrdot$ |
| \le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq |
$\le$, $\leq$, $\lneq$, $\leqq$, $\nleq$, $\nleqq$, $\lneqq$, $\lvertneqq$ |
| \ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq |
$\ge$, $\geq$, $\gneq$, $\geqq$, $\ngeq$, $\ngeqq$, $\gneqq$, $\gvertneqq$ |
| \lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless |
$\lessgtr$, $\lesseqgtr$, $\lesseqqgtr$, $\gtrless$, $\gtreqless$, $\gtreqqless$ |
| \leqslant, \nleqslant, \eqslantless |
$\leqslant$, $\nleqslant$, $\eqslantless$ |
| \geqslant, \ngeqslant, \eqslantgtr |
$\geqslant$, $\ngeqslant$, $\eqslantgtr$ |
| \lesssim, \lnsim, \lessapprox, \lnapprox |
$\lesssim$, $\lnsim$, $\lessapprox$, $\lnapprox$ |
| \gtrsim, \gnsim, \gtrapprox, \gnapprox |
$\gtrsim$, $\gnsim$, $\gtrapprox$, $\gnapprox$ |
| \prec, \nprec, \preceq, \npreceq, \precneqq |
$\prec$, $\nprec$, $\preceq$, $\npreceq$, $\precneqq$ |
| \succ, \nsucc, \succeq, \nsucceq, \succneqq |
$\succ$, $\nsucc$, $\succeq$, $\nsucceq$, $\succneqq$ |
| \preccurlyeq, \curlyeqprec |
$\preccurlyeq$, $\curlyeqprec$ |
| \succcurlyeq, \curlyeqsucc |
$\succcurlyeq$, $\curlyeqsucc$ |
| \precsim, \precnsim, \precapprox, \precnapprox |
$\precsim$, $\precnsim$, $\precapprox$, $\precnapprox$ |
| \succsim, \succnsim, \succapprox, \succnapprox |
$\succsim$, $\succnsim$, $\succapprox$, $\succnapprox$ |
几何符号
| \parallel, \nparallel, \shortparallel, \nshortparallel |
$\parallel$, $\nparallel$, $\shortparallel$, $\nshortparallel$ |
| \perp, \angle, \sphericalangle, \measuredangle, 45^\circ |
$\perp$, $\angle$, $\sphericalangle$, $\measuredangle$, $45^\circ$ |
| \Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar |
$\Box$, $\blacksquare$, $\diamond$, $\Diamond \lozenge$, $\blacklozenge$, $\bigstar$ |
| \bigcirc, \triangle, \bigtriangleup, \bigtriangledown |
$\bigcirc$, $\triangle$, $\bigtriangleup$, $\bigtriangledown$ |
| \vartriangle, \triangledown |
$\vartriangle$, $\triangledown$ |
| \blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright |
$\blacktriangle$, $\blacktriangledown$, $\blacktriangleleft$, $\blacktriangleright$ |
逻辑符号
| \forall, \exists, \nexists |
$\forall$, $\exists$, $\nexists$ |
| \therefore, \because, \And |
$\therefore$, $\because$, $\And$ |
| \or \lor \vee, \curlyvee, \bigvee |
$\or \lor \vee$, $\curlyvee$, $\bigvee$ |
| \and \land \wedge, \curlywedge, \bigwedge |
$\and \land \wedge$, $\curlywedge$, $\bigwedge$ |
| \bar{q}, \bar{abc}, \overline{q}, \overline{abc},
\lnot \neg, \not\operatorname{R}, \bot, \top |
$\bar{q}$, $\bar{abc}$, $\overline{q}$, $\overline{abc}$,
$\lnot \neg$, $\not\operatorname{R}$, $\bot$, $\top$ |
| \vdash \dashv, \vDash, \Vdash, \models |
$\vdash \dashv$, $\vDash$, $\Vdash$, $\models$ |
| \Vvdash \nvdash \nVdash \nvDash \nVDash |
$\Vvdash \nvdash \nVdash \nvDash \nVDash$ |
| \ulcorner \urcorner \llcorner \lrcorner |
$\ulcorner \urcorner \llcorner \lrcorner$ |
箭头
| \Rrightarrow, \Lleftarrow |
$\Rrightarrow$, $\Lleftarrow$ |
| \Rightarrow, \nRightarrow, \Longrightarrow \implies |
$\Rightarrow$, $\nRightarrow$, $\Longrightarrow \implies$ |
| \Leftarrow, \nLeftarrow, \Longleftarrow |
$\Leftarrow$, $\nLeftarrow$, $\Longleftarrow$ |
| \Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff |
$\Leftrightarrow$, $\nLeftrightarrow$, $\Longleftrightarrow \iff$ |
| \Uparrow, \Downarrow, \Updownarrow |
$\Uparrow, \Downarrow, \Updownarrow$ |
| \rightarrow \to, \nrightarrow, \longrightarrow |
$\rightarrow \to, \nrightarrow, \longrightarrow$ |
| \leftarrow \gets, \nleftarrow, \longleftarrow |
$\leftarrow \gets, \nleftarrow, \longleftarrow$ |
| \leftrightarrow, \nleftrightarrow, \longleftrightarrow |
$\leftrightarrow, \nleftrightarrow, \longleftrightarrow$ |
| \uparrow, \downarrow, \updownarrow |
$\uparrow, \downarrow, \updownarrow$ |
| \nearrow, \swarrow, \nwarrow, \searrow |
$\nearrow, \swarrow, \nwarrow, \searrow$ |
| \mapsto, \longmapsto |
$\mapsto, \longmapsto$ |
| \rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons |
$\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons$ |
| \curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright |
$\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright$ |
| \curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft |
$\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft$ |
| \hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow |
$\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow$ |
| 功能 | 语法 | 效果 |
|---|
| 上标 |
a^2/td>
| $a^2$ |
| 下标 |
a_2 |
$a_2 $ |
| 组合 |
a^{2+2}, a_{i,j} |
$a^{2+2}, a_{i,j}$ |
| 结合上下标 |
x_2^3 |
$x_2^3$ |
| 前置上下标 |
{}_1^2\!X_3^4 |
${}_1^2\!X_3^4$ |
| 导数 |
x', x^\prime, x\prime |
$x', x^\prime, x\prime$ |
| 导数点 |
\dot{x}, \ddot{y} |
$\dot{x}, \ddot{y}$ |
| 向量 |
\vec{c}, \overleftarrow{a b}, \overrightarrow{c d}, \overleftrightarrow{a b}, \widehat{e f g} |
$\vec{c}, \overleftarrow{a b}, \overrightarrow{c d}, \overleftrightarrow{a b}, \widehat{e f g}$ |
| 上弧 |
\overset{\frown} {AB} |
$\overset{\frown} {AB}$ |
| 上划线 |
\overline{h i j} |
$\overline{h i j}$ |
| 下划线 |
\underline{k l m} |
$\underline{k l m}$ |
| 上括号 |
\overbrace{1+2+\cdots+100}, \ begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix} |
$\overbrace{1+2+\cdots+100}, \begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}$ |
| 下括号 |
\underbrace{a+b+\cdots+z}, \ begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix} |
$\underbrace{a+b+\cdots+z}, \begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}$ |
| 求和 |
\sum_{k=1}^N k^2, \ begin{matrix} \sum_{k=1}^N k^2 \end{matrix} |
$\sum_{k=1}^N k^2, \begin{matrix} \sum_{k=1}^N k^2 \end{matrix}$ |
| 求积 |
\prod_{i=1}^N x_i, \ begin{matrix} \prod_{i=1}^N x_i \end{matrix} |
$\prod_{i=1}^N x_i, \begin{matrix} \prod_{i=1}^N x_i \end{matrix}$ |
| 上积 |
\coprod_{i=1}^N x_i, \ begin{matrix} \coprod_{i=1}^N x_i \end{matrix} |
$\coprod_{i=1}^N x_i, \begin{matrix} \coprod_{i=1}^N x_i \end{matrix}$ |
| 极限 |
\lim_{n \to \infty}x_n, \ begin{matrix} \lim_{n \to \infty}x_n \end{matrix} |
$\lim_{n \to \infty}x_n, \begin{matrix} \lim_{n \to \infty}x_n \end{matrix}$ |
| 积分 |
\int_{-N}^{N} e^x\, \mathrm{d}x, \ begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix} |
$\int_{-N}^{N} e^x\, \mathrm{d}x, \begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}$ |
| 双重积分 |
\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y |
$\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y$ |
| 三重积分 |
\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z |
$\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z$ |
| 四重积分 |
\iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t |
$\iiiint_{F}^{U} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z\,\mathrm{d}t$ |
| 闭合的曲綫、曲面积分 |
\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y |
$\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y$ |
| 交集 |
\bigcap_1^{n} p |
$\bigcap_1^{n} p$ |
| 并集 |
\bigcup_1^{k} p |
$\bigcup_1^{k} p$ |
| 功能 | 语法 | 效果 |
|---|
| 分数 |
\frac{2}{4}=0.5 |
$\frac{2}{4}=0.5$ |
| \tfrac{2}{4} = 0.5 |
$\tfrac{2}{4} = 0.5$ |
| \cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a |
$\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a$ |
| \dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a |
$\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a$ |
| 二项式系数 |
\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| \tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| \binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r} |
$\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}$ |
| 矩阵 |
\ begin{matrix}
x & y \\
z & v
\end{matrix} |
$\begin{matrix}
x & y \\
z & v
\end{matrix}$ |
| \ begin{vmatrix}
x & y \\
z & v
\end{vmatrix} |
$\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}$ |
| \ begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix} |
$\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}$ |
| \ begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix} |
$\begin{bmatrix}
0 & \cdots & 0 \\
\vdots & \ddots & \vdots \\
0 & \cdots & 0
\end{bmatrix}$ |
| \ begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix} |
$\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}$ |
| \ begin{pmatrix}
x & y \\
z & v
\end{pmatrix} |
$\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}$ |
| \bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr) |
$\bigl( \begin{smallmatrix}
a&b\\ c&d
\end{smallmatrix} \bigr)$ |
| 条件定义 |
f(n) =
\ begin{cases}
n/2, & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases} |
$f(n) =
\begin{cases}
n/2, & \mbox{if }n\mbox{ is even} \\
3n+1, & \mbox{if }n\mbox{ is odd}
\end{cases}$ |
| 多行等式、同餘式 |
\ begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align} |
$\begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align}$ |
| \ begin{align}
3^{6n+3}+4^{6n+3}
& \equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\
& \equiv 27^{2n+1}+64^{2n+1}\\
& \equiv 27^{2n+1}+(-27)^{2n+1}\\
& \equiv 27^{2n+1}-27^{2n+1}\\
& \equiv 0 \pmod{91}\\
\end{align} |
$\begin{align}
3^{6n+3}+4^{6n+3}
& \equiv (3^3)^{2n+1}+(4^3)^{2n+1}\\
& \equiv 27^{2n+1}+64^{2n+1}\\
& \equiv 27^{2n+1}+(-27)^{2n+1}\\
& \equiv 27^{2n+1}-27^{2n+1}\\
& \equiv 0 \pmod{91}\\
\end{align}$ |
| \ begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat} |
$\begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat}$ |
| \ begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array} |
$\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}$ |
| \ begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array} |
$\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}$ |
| 长公式换行 |
< math>f(x) \,\!
< math>= \sum_{n=0}^\infty a_n x^n
< math>= a_0+a_1x+a_2x^2+\cdots |
|
| 方程组 |
\ begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases} |
$\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}$ |
| 数组 |
\ begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array} |
$\begin{array}{|c|c||c|} a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}$ |