Latex公式总结

2023-11-12 20:47:22



完整文档

！待整理

参考*的数学公式教程
参考Cmd Markdown 公式指导手册

本文为 MathJax 在 Markdown 环境下的语法指引。

如何插入公式

\(\LaTeX\) 的数学公式有两种：行中公式和独立公式（行间公式）。行中公式放在文中与其它文字混编，独立公式单独成行。

行中公式可以用如下方法表示：

$ 数学公式 $

独立公式可以用如下方法表示：

$$ 数学公式 $$

函数、符号及特殊字符

声调 / 变音符号

\dot{a}, \ddot{a}, \acute{a}, \grave{a}

\[{\displaystyle {\dot {a}},{\ddot {a}},{\acute {a}},{\grave {a}}} \]

\check{a}, \breve{a}, \tilde{a}, \bar{a}

\[{\displaystyle {\check {a}},{\breve {a}},{\tilde {a}},{\bar {a}}} \]

\hat{a}, \widehat{a}, \vec{a}

\[{\displaystyle {\hat {a}},{\widehat {a}},{\vec {a}}} \]

标准函数

指数

\exp_a b = a^b, \exp b = e^b, 10^m

\[{\displaystyle \exp _{a}b=a^{b},\exp b=e^{b},10^{m}} \]

对数

\ln c, \lg d = \log e, \log_{10} f

\[{\displaystyle \ln c,\lg d=\log e,\log _{10}f} \]

三角函数

\sin a, \cos b, \tan c, \cot d, \sec e, \csc f

\[{\displaystyle \sin a,\cos b,\tan c,\cot d,\sec e,\csc f} \]

\arcsin a, \arccos b, \arctan c

\[{\displaystyle \arcsin a,\arccos b,\arctan c} \]

\arccot d, \arcsec e, \arccsc f

\[{\displaystyle \operatorname {arccot} d,\operatorname {arcsec} e,\operatorname {arccsc} f} \]

\sinh a, \cosh b, \tanh c, \coth d

\[{\displaystyle \sinh a,\cosh b,\tanh c,\coth d} \]

\operatorname{sh}k, \operatorname{ch}l, \operatorname{th}m, \operatorname{coth}n

\[{\displaystyle \operatorname {sh} k,\operatorname {ch} l,\operatorname {th} m,\operatorname {coth} n} \]

\operatorname{argsh}o, \operatorname{argch}p, \operatorname{argth}q

\[{\displaystyle \operatorname {argsh} o,\operatorname {argch} p,\operatorname {argth} q} \]

符号函数，绝对值

\sgn r, \left\vert s \right\vert

\[{\displaystyle \operatorname {sgn} r,\left\vert s\right\vert } \]

最大值，最小值

\min(x,y), \max(x,y)

\[{\displaystyle \min(x,y),\max(x,y)} \]

界限，极限

\min x, \max y, \inf s, \sup t

\[{\displaystyle \min x,\max y,\inf s,\sup t} \]

\lim u, \liminf v, \limsup w

\[{\displaystyle \lim u,\liminf v,\limsup w} \]

\lim_{x \to \infty} \frac{1}{n(n+1)}

\[{\displaystyle \lim_{x \to \infty} \frac{1}{n(n+1)}} \]

\dim p, \deg q, \det m, \ker\phi

\[{\displaystyle \dim p,\deg q,\det m,\ker \phi} \]

投射

\Pr j, \hom l, \lVert z \rVert, \arg z

\[{\displaystyle \Pr j,\hom l,\lVert z\rVert ,\arg z} \]

微分及导数

dt, \mathrm{d}t, \partial t, \nabla\psi

\[{\displaystyle dt,\mathrm {d} t,\partial t,\nabla \psi } \]

dy/dx, \mathrm{d}y/\mathrm{d}x, \frac{dy}{dx}, \frac{\mathrm{d}y}{\mathrm{d}x}, \frac{\partial^2}{\partial x_1\partial x_2}y

\[{\displaystyle dy/dx,\mathrm {d} y/\mathrm {d} x,{\frac {dy}{dx}},{\frac {\mathrm {d} y}{\mathrm {d} x}},{\frac {\partial ^{2}}{\partial x_{1}\partial x_{2}}}y} \]

\prime, \backprime, f^\prime, f', f'', f^{(3)}, \dot y, \ddot y

\[{\displaystyle \prime ,\backprime ,f^{\prime},f',f'',f^{(3)}\!,{\dot {y}},{\ddot {y}}} \]

类字母符号及常数

\infty, \aleph, \complement, \backepsilon, \eth, \Finv, \hbar

\[{\displaystyle \infty ,\aleph ,\complement ,\backepsilon ,\eth ,\Finv ,\hbar} \]

\Im, \imath, \jmath, \Bbbk, \ell, \mho, \wp, \Re, \circledS

\[{\displaystyle \Im ,\imath ,\jmath ,\Bbbk ,\ell ,\mho ,\wp ,\Re ,\circledS } \]

模运算

s_k \equiv 0 \pmod{m}

\[{\displaystyle s_{k}\equiv 0{\pmod {m}}} \]

a \bmod b

\[{\displaystyle a \bmod b} \]

\gcd(m, n), \operatorname{lcm}(m, n)

\[{\displaystyle \gcd(m,n),\operatorname {lcm} (m,n)} \]

\mid, \nmid, \shortmid, \nshortmid

\[{\displaystyle \mid ,\nmid ,\shortmid ,\nshortmid} \]

根号

\surd, \sqrt{2}, \sqrt[n]{}, \sqrt[3]{\frac{x^3+y^3}{2}}

\[{\displaystyle \surd ,{\sqrt {2}},{\sqrt[{n}]{}},{\sqrt[{3}]{\frac {x^{3}+y^{3}}{2}}}} \]

运算符

+, -, \pm, \mp, \dotplus

\[{\displaystyle +,-,\pm ,\mp ,\dotplus} \]

\times, \div, \divideontimes, /, \backslash

\[{\displaystyle \times ,\div ,\divideontimes ,/,\backslash} \]

\cdot, * \ast, \star, \circ, \bullet

\[{\displaystyle \cdot ,*\ast ,\star ,\circ ,\bullet} \]

\boxplus, \boxminus, \boxtimes, \boxdot

\[{\displaystyle \boxplus ,\boxminus ,\boxtimes ,\boxdot} \]

\oplus, \ominus, \otimes, \oslash, \odot

\[{\displaystyle \oplus ,\ominus ,\otimes ,\oslash ,\odot} \]

\circleddash, \circledcirc, \circledast

\[{\displaystyle \circleddash ,\circledcirc ,\circledast} \]

\bigoplus, \bigotimes, \bigodot

\[{\displaystyle \bigoplus ,\bigotimes ,\bigodot} \]

集合

\{ \}, \O \empty \emptyset, \varnothing

\[{\displaystyle \{\},\emptyset \emptyset \emptyset ,\varnothing } \]

\in, \notin \not\in, \ni, \not\ni

\[{\displaystyle \in ,\notin \not \in ,\ni ,\not \ni} \]

\cap, \Cap, \sqcap, \bigcap

\[{\displaystyle \cap ,\Cap ,\sqcap ,\bigcap} \]

\cup, \Cup, \sqcup, \bigcup, \bigsqcup, \uplus, \biguplus

\[{\displaystyle \cup ,\Cup ,\sqcup ,\bigcup ,\bigsqcup ,\uplus ,\biguplus} \]

\setminus, \smallsetminus, \times

\[{\displaystyle \setminus ,\smallsetminus ,\times} \]

\subset, \Subset, \sqsubset

\[{\displaystyle \subset ,\Subset ,\sqsubset} \]

\supset, \Supset, \sqsupset

\[{\displaystyle \supset ,\Supset ,\sqsupset} \]

\subseteq, \nsubseteq, \subsetneq, \varsubsetneq, \sqsubseteq

\[{\displaystyle \subseteq ,\nsubseteq ,\subsetneq ,\varsubsetneq ,\sqsubseteq} \]

\supseteq, \nsupseteq, \supsetneq, \varsupsetneq, \sqsupseteq

\[{\displaystyle \supseteq ,\nsupseteq ,\supsetneq ,\varsupsetneq ,\sqsupseteq} \]

\subseteqq, \nsubseteqq, \subsetneqq, \varsubsetneqq

\[{\displaystyle \subseteqq ,\nsubseteqq ,\subsetneqq ,\varsubsetneqq} \]

\supseteqq, \nsupseteqq, \supsetneqq, \varsupsetneqq

\[{\displaystyle \supseteqq ,\nsupseteqq ,\supsetneqq ,\varsupsetneqq} \]

关系符号

=, \ne, \neq, \equiv, \not\equiv

\[{\displaystyle =,\neq ,\neq ,\equiv ,\not \equiv} \]

\doteq, \doteqdot, \overset{\underset{\mathrm{def}}{}}{=}, :=

\[{\displaystyle \doteq ,\doteqdot ,{\overset {\underset {\mathrm {def} }{}}{=}},:=} \]

\sim, \nsim, \backsim, \thicksim, \simeq, \backsimeq, \eqsim, \cong, \ncong

\[{\displaystyle \sim ,\nsim ,\backsim ,\thicksim ,\simeq ,\backsimeq ,\eqsim ,\cong ,\ncong} \]

\approx, \thickapprox, \approxeq, \asymp, \propto, \varpropto

\[{\displaystyle \approx ,\thickapprox ,\approxeq ,\asymp ,\propto ,\varpropto} \]

<, \nless, \ll, \not\ll, \lll, \not\lll, \lessdot

\[{\displaystyle <,\nless ,\ll ,\not \ll ,\lll ,\not \lll ,\lessdot} \]

>, \ngtr, \gg, \not\gg, \ggg, \not\ggg, \gtrdot

\[{\displaystyle>,\ngtr ,\gg ,\not \gg ,\ggg ,\not \ggg ,\gtrdot } \]

\le, \leq, \lneq, \leqq, \nleq, \nleqq, \lneqq, \lvertneqq

\[{\displaystyle \leq ,\leq ,\lneq ,\leqq ,\nleq ,\nleqq ,\lneqq ,\lvertneqq} \]

\ge, \geq, \gneq, \geqq, \ngeq, \ngeqq, \gneqq, \gvertneqq

\[{\displaystyle \geq ,\geq ,\gneq ,\geqq ,\ngeq ,\ngeqq ,\gneqq ,\gvertneqq} \]

\lessgtr, \lesseqgtr, \lesseqqgtr, \gtrless, \gtreqless, \gtreqqless

\[{\displaystyle \lessgtr ,\lesseqgtr ,\lesseqqgtr ,\gtrless ,\gtreqless ,\gtreqqless} \]

\leqslant, \nleqslant, \eqslantless

\[{\displaystyle \leqslant ,\nleqslant ,\eqslantless} \]

\geqslant, \ngeqslant, \eqslantgtr

\[{\displaystyle \geqslant ,\ngeqslant ,\eqslantgtr} \]

\lesssim, \lnsim, \lessapprox, \lnapprox

\[{\displaystyle \lesssim ,\lnsim ,\lessapprox ,\lnapprox} \]

\gtrsim, \gnsim, \gtrapprox, \gnapprox

\[{\displaystyle \gtrsim ,\gnsim ,\gtrapprox ,\gnapprox} \]

\prec, \nprec, \preceq, \npreceq, \precneqq

\[{\displaystyle \prec ,\nprec ,\preceq ,\npreceq ,\precneqq} \]

\succ, \nsucc, \succeq, \nsucceq, \succneqq

\[{\displaystyle \succ ,\nsucc ,\succeq ,\nsucceq ,\succneqq} \]

\preccurlyeq, \curlyeqprec

\[{\displaystyle \preccurlyeq ,\curlyeqprec} \]

\succcurlyeq, \curlyeqsucc

\[{\displaystyle \succcurlyeq ,\curlyeqsucc} \]

\precsim, \precnsim, \precapprox, \precnapprox

\[{\displaystyle \precsim ,\precnsim ,\precapprox ,\precnapprox} \]

\succsim, \succnsim, \succapprox, \succnapprox

\[{\displaystyle \succsim ,\succnsim ,\succapprox ,\succnapprox} \]

几何符号

\parallel, \nparallel, \shortparallel, \nshortparallel

\[{\displaystyle \parallel ,\nparallel ,\shortparallel ,\nshortparallel} \]

\perp, \angle, \sphericalangle, \measuredangle, 45^\circ

\[{\displaystyle \perp ,\angle ,\sphericalangle ,\measuredangle ,45^{\circ}} \]

\Box, \blacksquare, \diamond, \Diamond \lozenge, \blacklozenge, \bigstar

\[{\displaystyle \Box ,\blacksquare ,\diamond ,\Diamond \lozenge ,\blacklozenge ,\bigstar} \]

\bigcirc, \triangle, \bigtriangleup, \bigtriangledown

\[{\displaystyle \bigcirc ,\triangle ,\bigtriangleup ,\bigtriangledown} \]

\vartriangle, \triangledown

\[{\displaystyle \vartriangle ,\triangledown} \]

\blacktriangle, \blacktriangledown, \blacktriangleleft, \blacktriangleright

\[{\displaystyle \blacktriangle ,\blacktriangledown ,\blacktriangleleft ,\blacktriangleright} \]

逻辑符号

\forall, \exists, \nexists

\[{\displaystyle \forall ,\exists ,\nexists} \]

\therefore, \because, \And

\[{\displaystyle \therefore ,\because ,\And} \]

\or \lor \vee, \curlyvee, \bigvee

\[{\displaystyle \lor ,\lor ,\vee ,\curlyvee ,\bigvee} \]

\and \land \wedge, \curlywedge, \bigwedge

\[{\displaystyle \land ,\land ,\wedge ,\curlywedge ,\bigwedge} \]

\bar{q}, \bar{abc}, \overline{q}, \overline{abc},

\lnot \neg, \not\operatorname{R}, \bot, \top

\[{\displaystyle {\bar {q}},{\bar {abc}},{\overline {q}},{\overline {abc}},} \]

\[{\displaystyle \lnot \neg ,\not \operatorname {R} ,\bot ,\top } \]

\vdash \dashv, \vDash, \Vdash, \models

\[{\displaystyle \vdash ,\dashv ,\vDash ,\Vdash ,\models} \]

\Vvdash \nvdash \nVdash \nvDash \nVDash

\[{\displaystyle \Vvdash ,\nvdash ,\nVdash ,\nvDash ,\nVDash} \]

\ulcorner \urcorner \llcorner \lrcorner

\[{\displaystyle \ulcorner \urcorner \llcorner \lrcorner} \]

箭头

\Rrightarrow, \Lleftarrow

\[{\displaystyle \Rrightarrow ,\Lleftarrow} \]

\Rightarrow, \nRightarrow, \Longrightarrow \implies

\[{\displaystyle \Rightarrow ,\nRightarrow ,\Longrightarrow ,\implies} \]

\Leftarrow, \nLeftarrow, \Longleftarrow

\[{\displaystyle \Leftarrow ,\nLeftarrow ,\Longleftarrow} \]

\Leftrightarrow, \nLeftrightarrow, \Longleftrightarrow \iff

\[{\displaystyle \Leftrightarrow ,\nLeftrightarrow ,\Longleftrightarrow \iff} \]

\Uparrow, \Downarrow, \Updownarrow

\[{\displaystyle \Uparrow ,\Downarrow ,\Updownarrow} \]

\rightarrow \to, \nrightarrow, \longrightarrow

\[{\displaystyle \rightarrow \to ,\nrightarrow ,\longrightarrow} \]

\leftarrow \gets, \nleftarrow, \longleftarrow

\[{\displaystyle \leftarrow \gets ,\nleftarrow ,\longleftarrow} \]

\leftrightarrow, \nleftrightarrow, \longleftrightarrow

\[{\displaystyle \leftrightarrow ,\nleftrightarrow ,\longleftrightarrow} \]

\uparrow, \downarrow, \updownarrow

\[{\displaystyle \uparrow ,\downarrow ,\updownarrow} \]

\nearrow, \swarrow, \nwarrow, \searrow

\[{\displaystyle \nearrow ,\swarrow ,\nwarrow ,\searrow} \]

\mapsto, \longmapsto

\[{\displaystyle \mapsto ,\longmapsto} \]

\rightharpoonup \rightharpoondown \leftharpoonup \leftharpoondown \upharpoonleft \upharpoonright \downharpoonleft \downharpoonright \rightleftharpoons \leftrightharpoons

\[{\displaystyle \rightharpoonup ,\rightharpoondown ,\leftharpoonup ,\leftharpoondown ,\upharpoonleft ,\upharpoonright ,\downharpoonleft ,\downharpoonright ,\rightleftharpoons ,\leftrightharpoons} \]

\curvearrowleft \circlearrowleft \Lsh \upuparrows \rightrightarrows \rightleftarrows \rightarrowtail \looparrowright

\[{\displaystyle \curvearrowleft ,\circlearrowleft ,\Lsh ,\upuparrows ,\rightrightarrows ,\rightleftarrows ,\rightarrowtail ,\looparrowright} \]

\curvearrowright \circlearrowright \Rsh \downdownarrows \leftleftarrows \leftrightarrows \leftarrowtail \looparrowleft

\[{\displaystyle \curvearrowright ,\circlearrowright ,\Rsh ,\downdownarrows ,\leftleftarrows ,\leftrightarrows ,\leftarrowtail ,\looparrowleft} \]

\hookrightarrow \hookleftarrow \multimap \leftrightsquigarrow \rightsquigarrow \twoheadrightarrow \twoheadleftarrow

\[{\displaystyle \hookrightarrow ,\hookleftarrow ,\multimap ,\leftrightsquigarrow ,\rightsquigarrow ,\twoheadrightarrow ,\twoheadleftarrow} \]

特殊符号

省略号：数学公式中常见的省略号有两种，\ldots 表示与文本底线对齐的省略号，\cdots 表示与文本中线对齐的省略号。

\amalg \% \dagger \ddagger \ldots \cdots

\[{\displaystyle \amalg \%\dagger \ddagger \ldots \cdots} \]

\smile \frown \wr \triangleleft \triangleright

\[{\displaystyle \smile \frown \wr \triangleleft \triangleright} \]

\diamondsuit, \heartsuit, \clubsuit, \spadesuit, \Game, \flat, \natural, \sharp

\[{\displaystyle \diamondsuit ,\heartsuit ,\clubsuit ,\spadesuit ,\Game ,\flat ,\natural ,\sharp} \]

未分类

\diagup \diagdown \centerdot \ltimes \rtimes \leftthreetimes \rightthreetimes

\[{\displaystyle \diagup ,\diagdown ,\centerdot ,\ltimes ,\rtimes ,\leftthreetimes ,\rightthreetimes} \]

\eqcirc \circeq \triangleq \bumpeq \Bumpeq \doteqdot \risingdotseq \fallingdotseq

\[{\displaystyle \eqcirc ,\circeq ,\triangleq ,\bumpeq ,\Bumpeq ,\doteqdot ,\risingdotseq ,\fallingdotseq} \]

\intercal \barwedge \veebar \doublebarwedge \between \pitchfork

\[{\displaystyle \intercal ,\barwedge ,\veebar ,\doublebarwedge ,\between ,\pitchfork} \]

\vartriangleleft \ntriangleleft \vartriangleright \ntriangleright

\[{\displaystyle \vartriangleleft ,\ntriangleleft ,\vartriangleright ,\ntriangleright} \]

\trianglelefteq \ntrianglelefteq \trianglerighteq \ntrianglerighteq

\[{\displaystyle \trianglelefteq ,\ntrianglelefteq ,\trianglerighteq ,\ntrianglerighteq} \]

关于这些符号的更多语义，参阅 TeX Cookbook 的简述。

上标、下标及积分等

功能|语法|效果

^ 表示上标, _ 表示下标。如果上下标的内容多于一个字符，需要用 {} 将这些内容括成一个整体。上下标可以嵌套，也可以同时使用。

上标

a^2

\[{\displaystyle a^{2}} \]

下标

a_2

\[{\displaystyle a_{2}} \]

组合

a^{2+2}

\[{\displaystyle a^{2+2}} \]

a_{i,j}

\[{\displaystyle a_{i,j}} \]

结合上下标

x_2^3

\[{\displaystyle x_{2}^{3}} \]

前置上下标

{}_1^2\!X_3^4

\[{\displaystyle {}_{1}^{2}\!X_{3}^{4}} \]

导数（HTML）

x'

\[{\displaystyle x'} \]

导数（PNG）

x^\prime

\[{\displaystyle x^{\prime}} \]

导数（错误）

x\prime

\[{\displaystyle x\prime} \]

导数点

\dot{x}

\[{\displaystyle {\dot {x}}} \]

\ddot{y}

\[{\displaystyle {\ddot {y}}} \]

向量

\vec{c}（只有一个字母）

\[{\displaystyle {\vec {c}}} \]

\overleftarrow{a b}

\[{\displaystyle {\overleftarrow {ab}}} \]

\overrightarrow{c d}

\[{\displaystyle {\overrightarrow {cd}}} \]

\overleftrightarrow{a b}

\[{\displaystyle {\overleftrightarrow {ab}}} \]

\widehat{e f g}

\[{\displaystyle {\widehat {efg}}} \]

上弧

（注: 正确应该用 \overarc，但在这里行不通。要用建议的语法作为解决办法。）（使用 \ overarc 时需要引入 {arcs} 包。）

\overset{\frown} {AB}

\[{\displaystyle {\overset {\frown}{AB}}} \]

上划线

\overline{h i j}

\[{\displaystyle {\overline {hij}}} \]

下划线

\underline{k l m}

\[{\displaystyle {\underline {klm}}} \]

上括号

\overbrace{1+2+\cdots+100}

\[{\displaystyle \overbrace {1+2+\cdots +100} } \]

\begin{matrix} 5050 \\ \overbrace{ 1+2+\cdots+100 } \end{matrix}

\[{\displaystyle {\begin{matrix}5050\\\overbrace {1+2+\cdots +100} \end{matrix}}} \]

下括号

\underbrace{a+b+\cdots+z}

\[{\displaystyle \underbrace {a+b+\cdots +z} } \]

\begin{matrix} \underbrace{ a+b+\cdots+z } \\ 26 \end{matrix}

\[{\displaystyle {\begin{matrix}\underbrace {a+b+\cdots +z} \\26\end{matrix}}} \]

求和（累加）

\sum_{k=1}^N k^2

\[{\displaystyle \sum _{k=1}^{N}k^{2}} \]

\begin{matrix} \sum_{k=1}^N k^2 \end{matrix}

\[{\displaystyle {\begin{matrix}\sum _{k=1}^{N}k^{2}\end{matrix}}} \]

求积（累乘）

\prod_{i=1}^N x_i

\[{\displaystyle \prod _{i=1}^{N}x_{i}} \]

\begin{matrix} \prod_{i=1}^N x_i \end{matrix}

\[{\displaystyle {\begin{matrix}\prod _{i=1}^{N}x_{i}\end{matrix}}} \]

上积

\coprod_{i=1}^N x_i

\[{\displaystyle \coprod _{i=1}^{N}x_{i}} \]

\begin{matrix} \coprod_{i=1}^N x_i \end{matrix}

\[{\displaystyle {\begin{matrix}\coprod _{i=1}^{N}x_{i}\end{matrix}}} \]

极限

\lim_{n \to \infty}x_n

\[{\displaystyle \lim _{n\to \infty}x_{n}} \]

\begin{matrix} \lim_{n \to \infty}x_n \end{matrix}

\[{\displaystyle {\begin{matrix}\lim _{n\to \infty }x_{n}\end{matrix}}} \]

积分

\int_{-N}^{N} e^x\, {\rm d}x

\[{\displaystyle \int _{-N}^{N}e^{x}\,{\rm d} x} \]

本例中 \, 和 {\rm d} 部分可省略，但建议加入，能使式子更美观。{\rm d}可以用\mathrm{d}等价替换。

\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}（矩阵中积分符号变小）

\[{\displaystyle {\begin{matrix}\int _{-N}^{N}e^{x}\,\mathrm {d} x\end{matrix}}} \]

双重积分

\iint_{D}^{W} \, \mathrm{d}x\,\mathrm{d}y

\[{\displaystyle \iint _{D}^{W}\,\mathrm {d} x\,\mathrm {d} y} \]

三重积分

\iiint_{E}^{V} \, \mathrm{d}x\,\mathrm{d}y\,\mathrm{d}z

\[{\displaystyle \iiint _{E}^{V}\,\mathrm {d} x\,\mathrm {d} y\,\mathrm {d} z} \]

闭合的曲线、曲面积分

\oint_{C} x^3\, \mathrm{d}x + 4y^2\, \mathrm{d}y

\[{\displaystyle \oint _{C}x^{3}\,\mathrm {d} x+4y^{2}\,\mathrm {d} y} \]

交集

\bigcap_1^{n} p

\[{\displaystyle \bigcap _{1}^{n}p} \]

并集

\bigcup_1^{k} p

\[{\displaystyle \bigcup _{1}^{k}p} \]

分数

通常使用 \frac {分子} {分母} 命令产生一个分数，分数可嵌套。
便捷情况可直接输入 \frac ab 来快速生成一个 \(\frac ab\) 。
如果分式很复杂，亦可使用 分子 \over 分母 命令，此时分数仅有一层。

功能|语法|效果

分数

\frac{2}{4}=0.5

\[{\displaystyle {\frac {2}{4}}=0.5} \]

小型分数

\tfrac{2}{4} = 0.5

\[{\displaystyle {\tfrac {2}{4}}=0.5} \]

连分式（大型嵌套分式）

\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a

\[{\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a} \]

大型不嵌套分式

\dfrac{2}{4} = 0.5 \qquad \dfrac{2}{c + \dfrac{2}{d + \dfrac{2}{4}}} = a

\[{\displaystyle {\dfrac {2}{4}}=0.5\qquad {\dfrac {2}{c+{\dfrac {2}{d+{\dfrac {2}{4}}}}}}=a} \]

二项式系数

\dbinom{n}{r}=\binom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}

\[{\displaystyle {\dbinom {n}{r}}={\binom {n}{n-r}}=\mathrm {C} _{n}^{r}=\mathrm {C} _{n}^{n-r}} \]

小型二项式系数

\tbinom{n}{r}=\tbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}

\[{\displaystyle {\tbinom {n}{r}}={\tbinom {n}{n-r}}=\mathrm {C} _{n}^{r}=\mathrm {C} _{n}^{n-r}} \]

大型二项式系数

\binom{n}{r}=\dbinom{n}{n-r}=\mathrm{C}_n^r=\mathrm{C}_n^{n-r}

\[{\displaystyle {\binom {n}{r}}={\dbinom {n}{n-r}}=\mathrm {C} _{n}^{r}=\mathrm {C} _{n}^{n-r}} \]

在以e为底的指数函数、极限和积分中尽量不要使用 \frac 符号：它会使整段函数看起来很怪，而且可能产生歧义。也正是因此它在专业数学排版中几乎从不出现。
横着写这些分式，中间使用斜线间隔 / （用斜线代替分数线）。

  • 例子：
\begin{array}{cc}
\mathrm{Bad} & \mathrm{Better} \\
\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}
  • 显示：

\[\begin{array}{cc} \mathrm{Bad} & \mathrm{Better} \\ \hline \\ e^{i\frac{\pi}2} \quad e^{\frac{i\pi}2}& e^{i\pi/2} \\ \int_{-\frac\pi2}^\frac\pi2 \sin x\,dx & \int_{-\pi/2}^{\pi/2}\sin x\,dx \\ \end{array} \]

矩阵、条件表达式、方程组

语法：

\begin{类型}
公式内容
\end{类型}

类型可以是：矩阵 matrix pmatrix bmatrix Bmatrix vmatrix Vmatrix、条件表达式 cases、多行对齐方程式 aligned、数组 array。

在公式内容中：在每一行中插入 & 来指定需要对齐的内容，在每行结尾处使用 \\ 换行。

无框矩阵

在开头使用 begin{matrix}，在结尾使用 end{matrix}，在中间插入矩阵元素，每个元素之间插入 & ，并在每行结尾处使用 \\ 。

\begin{matrix}
x & y \\
z & v
\end{matrix}

\[{\displaystyle {\begin{matrix}x&y\\z&v\end{matrix}}} \]

有框矩阵

在开头将 matrix 替换为 pmatrix bmatrix Bmatrix vmatrix Vmatrix 。

\begin{vmatrix}
x & y \\
z & v
\end{vmatrix}

\[{\displaystyle {\begin{vmatrix}x&y\\z&v\end{vmatrix}}} \]

\begin{Vmatrix}
x & y \\
z & v
\end{Vmatrix}

\[{\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}} \]

使用 \cdots \(\cdots\) , \ddots \(\ddots\) , \vdots \(\vdots\) 来输入省略符号。

\begin{bmatrix}
0      & \cdots & 0      \\
\vdots & \ddots & \vdots \\
0      & \cdots & 0
\end{bmatrix}

\[{\displaystyle {\begin{bmatrix}0&\cdots &0\\\vdots &\ddots &\vdots \\0&\cdots &0\end{bmatrix}}} \]

\begin{Bmatrix}
x & y \\
z & v
\end{Bmatrix}

\[{\displaystyle {\begin{Bmatrix}x&y\\z&v\end{Bmatrix}}} \]

\begin{pmatrix}
x & y \\
z & v
\end{pmatrix}

\[{\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}} \]

条件表达式

f(n) =
\begin{cases}
n/2,  & \text{if }n\text{ is even} \\
3n+1, & \text{if }n\text{ is odd}
\end{cases}

\[{\displaystyle f(n)={\begin{cases}n/2,&{\text{if }}n{\text{ is even}}\\3n+1,&{\text{if }}n{\text{ is odd}}\end{cases}}} \]

多行等式、同余式

人们经常想要一列整齐且居中的方程式序列。使用 \begin{aligned}…\end{aligned}。

\begin{aligned}
f(x) & = (m+n)^2 \\
     & = m^2+2mn+n^2 \\
\end{aligned}

\[{\displaystyle {\begin{aligned}f(x)&=(m+n)^{2}\\&=m^{2}+2mn+n^{2}\\\end{aligned}}} \]

begin{aligned}
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{aligned}

\[{\displaystyle {\begin{aligned}3^{6n+3}+4^{6n+3}&\equiv (3^{3})^{2n+1}+(4^{3})^{2n+1}\\&\equiv 27^{2n+1}+64^{2n+1}\\&\equiv 27^{2n+1}+(-27)^{2n+1}\\&\equiv 27^{2n+1}-27^{2n+1}\\&\equiv 0{\pmod {91}}\\\end{aligned}}} \]

\begin{alignedat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
     & = m^2-2mn+n^2 \\
\end{alignedat}

\[{\displaystyle {\begin{alignedat}{3}f(x)&=(m-n)^{2}\\f(x)&=(-m+n)^{2}\\&=m^{2}-2mn+n^{2}\\\end{alignedat}}} \]

方程组

\begin{cases}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}

\[${\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}$ \]

或

\left\{\begin{aligned}
3x + 5y +  z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{aligned}\right.

\[\left\{\begin{aligned} 3x + 5y + z \\ 7x - 2y + 4z \\ -6x + 3y + 2z \end{aligned}\right. \]

数组与表格

通常，一个格式化后的表格比单纯的文字或排版后的文字更具有可读性。数组和表格均以 \begin{array} 开头，并在其后定义列数及每一列的文本对齐属性，c l r 分别代表居中、左对齐及右对齐。若需要插入垂直分割线，在定义式中插入 | ，若要插入水平分割线，在下一行输入前插入 \hline 。与矩阵相似，每行元素间均须要插入 & ，每行元素以 \\ 结尾，最后以 \end{array} 结束数组。

  • 例子：
\begin{array}{c|lcr}
n & \text{左对齐} & \text{居中对齐} & \text{右对齐} \\
\hline
1 & 0.24 & 1 & 125 \\
2 & -1 & 189 & -8 \\
3 & -20 & 2000 & 1+10i
\end{array}
  • 显示：

\[\begin{array}{c|lcr} n & \text{左对齐} & \text{居中对齐} & \text{右对齐} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array} \]

  • 例子:
\begin{array}{lcl}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
  • 显示：

\[{\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} \]

  • 例子:
\begin{array}{lcr}
z        & = & a \\
f(x,y,z) & = & x + y + z
\end{array}
  • 显示:

\[{\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}} \]

  • 例子:
\begin{array}{ccc}
a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}
  • 显示:

\[${\displaystyle {\begin{array}{ccc}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}$ \]

嵌套数组或表格

多个数组/表格可 互相嵌套 并组成一组数组/一组表格。
使用嵌套前必须声明 $$ 符号。

  • 例子：
% outer vertical array of arrays 外层垂直表格
\begin{array}{c}
    % inner horizontal array of arrays 内层水平表格
    \begin{array}{cc}
        % inner array of minimum values 内层"最小值"数组
        \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 内层"最大值"数组
        \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}
    % 内层第一行表格组结束
    \\
    % inner array of delta values 内层第二行Delta值数组
        \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}
        % 内层第二行表格组结束
\end{array}
  • 显示：

\[% outer vertical array of arrays 外层垂直表格 \begin{array}{c} % inner horizontal array of arrays 内层水平表格 \begin{array}{cc} % inner array of minimum values 内层"最小值"数组 \begin{array}{c|cccc} \text{min} & 0 & 1 & 2 & 3\\ \hline 0 & 0 & 0 & 0 & 0\\ 1 & 0 & 1 & 1 & 1\\ 2 & 0 & 1 & 2 & 2\\ 3 & 0 & 1 & 2 & 3 \end{array} & % inner array of maximum values 内层"最大值"数组 \begin{array}{c|cccc} \text{max}&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 1 & 2 & 3\\ 2 & 2 & 2 & 2 & 3\\ 3 & 3 & 3 & 3 & 3 \end{array} \end{array} % 内层第一行表格组结束 \\ % inner array of delta values 内层第二行Delta值数组 \begin{array}{c|cccc} \Delta&0&1&2&3\\ \hline 0 & 0 & 1 & 2 & 3\\ 1 & 1 & 0 & 1 & 2\\ 2 & 2 & 1 & 0 & 1\\ 3 & 3 & 2 & 1 & 0 \end{array} % 内层第二行表格组结束 \end{array} \]

用数组实现带分割符号的矩阵

  • 例子：
$$
\left[
    \begin{array}{cc|c}
      1&2&3\\
      4&5&6
    \end{array}
\right]
$$
  • 显示：

\[\left[ \begin{array}{cc|c} 1&2&3\\ 4&5&6 \end{array} \right] \]

其中 cc|c 代表在一个三列矩阵中的第二和第三列之间插入分割线。

字体

希腊字母

输入 \小写希腊字母英文全称 和 \首字母大写希腊字母英文全称 来分别输入小写和大写希腊字母。

\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta

\[{\displaystyle \mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta } \]

\Iota \Kappa \Lambda \Mu \Nu \Xi \Omicron \Pi

\[{\displaystyle \mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \mathrm {O} \Xi \Pi } \]

\Rho \Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega

\[{\displaystyle \mathrm {P} \Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega } \]

\alpha \beta \gamma \delta \epsilon \zeta \eta \theta

\[{\displaystyle \alpha \beta \gamma \delta \epsilon \zeta \eta \theta} \]

\iota \kappa \lambda \mu \nu \omicron \xi \pi

\[{\displaystyle \iota \kappa \lambda \mu \nu \mathrm {o} \xi \pi } \]

\rho \sigma \tau \upsilon \phi \chi \psi \omega

\[{\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega} \]

部分字母有变量专用形式，以 \var- 开头。

\varepsilon \digamma \varkappa \varpi

\[{\displaystyle \varepsilon \digamma \varkappa \varpi} \]

\varrho \varsigma \vartheta \varphi

\[{\displaystyle \varrho \varsigma \vartheta \varphi} \]

希伯来符号

\aleph \beth \gimel \daleth

\[{\displaystyle \aleph \beth \gimel \daleth} \]

部分字体的简称

若要对公式的某一部分字符进行字体转换，可以用 {\字体 {需转换的部分字符}} 命令，其中 \字体 部分可以参照下表选择合适的字体。一般情况下，公式默认为意大利体 \(italic\) 。

输入 说明 显示 输入 说明 显示
\rm 罗马体 \(\rm{Sample}\) \cal 花体 \(\cal{SAMPLE}\)
\it 意大利体 \(\it{Sample}\) \Bbb 黑板粗体 \(\Bbb{SAMPLE}\)
\bf 粗体 \(\bf{Sample}\) \mit 数学斜体 \(\mit{SAMPLE}\)
\sf 等线体 \(\sf{Sample}\) \scr 手写体 \(\scr{SAMPLE}\)
\tt 打字机体 \(\tt{Sample}\) \frak 旧德式字体 \(\frak{Sample}\)

所有字体

黑板报粗体

\mathbb{ABCDEFGHI}

\[{\displaystyle \mathbb {ABCDEFGHI} } \]

\mathbb{JKLMNOPQR}

\[{\displaystyle \mathbb {JKLMNOPQR} } \]

\mathbb{STUVWXYZ}

\[{\displaystyle \mathbb {STUVWXYZ} } \]

粗体

\mathbf{ABCDEFGHI}

\[{\displaystyle \mathbf {ABCDEFGHI} } \]

\mathbf{JKLMNOPQR}

\[{\displaystyle \mathbf {JKLMNOPQR} } \]

\mathbf{STUVWXYZ}

\[{\displaystyle \mathbf {STUVWXYZ} } \]

\mathbf{abcdefghijklm}

\[{\displaystyle \mathbf {abcdefghijklm} } \]

\mathbf{nopqrstuvwxyz}

\[{\displaystyle \mathbf {nopqrstuvwxyz} } \]

\mathbf{0123456789}

\[{\displaystyle \mathbf {0123456789} } \]

粗体希腊字母

\boldsymbol{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}

\[{\displaystyle {\boldsymbol {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}} \]

\boldsymbol{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}

\[{\displaystyle {\boldsymbol {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}} \]

\boldsymbol{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}

\[{\displaystyle {\boldsymbol {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}} \]

\boldsymbol{\alpha\beta\gamma\delta\epsilon\zeta\eta\theta}

\[{\displaystyle {\boldsymbol {\alpha \beta \gamma \delta \epsilon \zeta \eta \theta}}} \]

\boldsymbol{\iota\kappa\lambda\mu\nu\xi\pi\rho}

\[{\displaystyle {\boldsymbol {\iota \kappa \lambda \mu \nu \xi \pi \rho}}} \]

\boldsymbol{\sigma\tau\upsilon\phi\chi\psi\omega}

\[{\displaystyle {\boldsymbol {\sigma \tau \upsilon \phi \chi \psi \omega}}} \]

\boldsymbol{\varepsilon\digamma\varkappa\varpi}

\[{\displaystyle {\boldsymbol {\varepsilon \digamma \varkappa \varpi}}} \]

\boldsymbol{\varrho\varsigma\vartheta\varphi}

\[{\displaystyle {\boldsymbol {\varrho \varsigma \vartheta \varphi}}} \]

斜体（拉丁字母默认）

\mathit{0123456789}

\[{\displaystyle {\mathit {0123456789}}} \]

斜体希腊字母（小写字母默认）

\mathit{\Alpha\Beta\Gamma\Delta\Epsilon\Zeta\Eta\Theta}

\[{\displaystyle {\mathit {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}} \]

\mathit{\Iota\Kappa\Lambda\Mu\Nu\Xi\Pi\Rho}

\[{\displaystyle {\mathit {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}} \]

\mathit{\Sigma\Tau\Upsilon\Phi\Chi\Psi\Omega}

\[{\displaystyle {\mathit {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}} \]

罗马体

\mathrm{ABCDEFGHI}

\[{\displaystyle \mathrm {ABCDEFGHI} } \]

\mathrm{JKLMNOPQR}

\[{\displaystyle \mathrm {JKLMNOPQR} } \]

\mathrm{STUVWXYZ}

\[{\displaystyle \mathrm {STUVWXYZ} } \]

\mathrm{abcdefghijklm}

\[{\displaystyle \mathrm {abcdefghijklm} } \]

\mathrm{nopqrstuvwxyz}

\[{\displaystyle \mathrm {nopqrstuvwxyz} } \]

\mathrm{0123456789}

\[{\displaystyle \mathrm {0123456789} } \]

无衬线体

\mathsf{ABCDEFGHI}

\[{\displaystyle {\mathsf {ABCDEFGHI}}} \]

\mathsf{JKLMNOPQR}

\[{\displaystyle {\mathsf {JKLMNOPQR}}} \]

\mathsf{STUVWXYZ}

\[{\displaystyle {\mathsf {STUVWXYZ}}} \]

\mathsf{abcdefghijklm}

\[{\displaystyle {\mathsf {abcdefghijklm}}} \]

\mathsf{nopqrstuvwxyz}

\[{\displaystyle {\mathsf {nopqrstuvwxyz}}} \]

\mathsf{0123456789}

\[{\displaystyle {\mathsf {0123456789}}} \]

无衬线体希腊字母（仅大写）

\mathsf{\Alpha \Beta \Gamma \Delta \Epsilon \Zeta \Eta \Theta}

\[{\displaystyle {\mathsf {\mathrm {A} \mathrm {B} \Gamma \Delta \mathrm {E} \mathrm {Z} \mathrm {H} \Theta }}} \]

\mathsf{\Iota \Kappa \Lambda \Mu \Nu \Xi \Pi \Rho}

\[{\displaystyle {\mathsf {\mathrm {I} \mathrm {K} \Lambda \mathrm {M} \mathrm {N} \Xi \Pi \mathrm {P} }}} \]

\mathsf{\Sigma \Tau \Upsilon \Phi \Chi \Psi \Omega}

\[{\displaystyle {\mathsf {\Sigma \mathrm {T} \Upsilon \Phi \mathrm {X} \Psi \Omega }}} \]

手写体 / 花体

\mathcal{ABCDEFGHI}

\[{\displaystyle {\mathcal {ABCDEFGHI}}} \]

\mathcal{JKLMNOPQR}

\[{\displaystyle {\mathcal {JKLMNOPQR}}} \]

\mathcal{STUVWXYZ}

\[{\displaystyle {\mathcal {STUVWXYZ}}} \]

Fraktur 体

\mathfrak{ABCDEFGHI}

\[{\displaystyle {\mathfrak {ABCDEFGHI}}} \]

\mathfrak{JKLMNOPQR}

\[{\displaystyle {\mathfrak {JKLMNOPQR}}} \]

\mathfrak{STUVWXYZ}

\[{\displaystyle {\mathfrak {STUVWXYZ}}} \]

\mathfrak{abcdefghijklm}

\[{\displaystyle {\mathfrak {abcdefghijklm}}} \]

\mathfrak{nopqrstuvwxyz}

\[{\displaystyle {\mathfrak {nopqrstuvwxyz}}} \]

\mathfrak{0123456789}

\[{\displaystyle {\mathfrak {0123456789}}} \]

小型手写体

{\scriptstyle\text{abcdefghijklm}}

\[{\displaystyle {\scriptstyle {\text{abcdefghijklm}}}} \]

混合字体

特征|语法|渲染效果

斜体字符（忽略空格）

x y z

\[{\displaystyle xyz} \]

非斜体字符

\text{x y z}

\[{\displaystyle {\text{x y z}}} \]

混合斜体（差）

\text{if} n \text{is even}

\[{\displaystyle {\text{if}}n{\text{is even}}} \]

混合斜体（好）

\text{if }n\text{ is even}

\[{\displaystyle {\text{if }}n{\text{ is even}}} \]

混合斜体（替代品：~ 或者 \ 强制空格）

\text{if}~n\ \text{is even}

\[{\displaystyle {\text{if}}~n\ {\text{is even}}} \]

注释文本

使用 \text {文字} 来添加注释文本（注释文本不会被识别为公式，不用斜体显示）。\text {文字}中仍可以使用 $公式$ 插入其它公式。

  • 例子：
f(n)= \begin{cases}
n/2, & \text {if $n$ is even} \\
3n+1, &\text{if $n$ is odd}
\end{cases}
  • 显示：

\[f(n)= \begin{cases} n/2, & \text {if}\ n\ \text{is even} \\ 3n+1, & \text {if}\ n\ \text{is odd} \end{cases} \]

括号

()、[] 和 | 表示符号本身，使用 \{\} 来表示 {} 。

功能|语法|显示

短括号

\frac{1}{2}

\[{\displaystyle ({\frac {1}{2}})} \]

长括号

\left(\frac{1}{2} \right

\[{\displaystyle \left({\frac {1}{2}}\right)} \]

使用 \left 和 \right 来创建自动匹配高度的 (圆括号)，[方括号] 和 {花括号} 。

功能|语法|显示

圆括号，小括号

\left( \frac{a}{b} \right)

\[{\displaystyle \left({\frac {a}{b}}\right)} \]

方括号，中括号

\left[ \frac{a}{b} \right]

\[{\displaystyle \left[{\frac {a}{b}}\right]} \]

花括号，大括号

\left{ \frac{a}{b} \right}

\[{\displaystyle \left\{{\frac {a}{b}}\right\}} \]

角括号

\left \langle \frac{a}{b} \right \rangle

\[{\displaystyle \left\langle {\frac {a}{b}}\right\rangle } \]

单竖线，绝对值

\left| \frac{a}{b} \right|

\[{\displaystyle \left| \frac{a}{b} \right|} \]

双竖线，范

\left \| \frac{a}{b} \right \|

\[{\displaystyle \left\|{\frac {a}{b}}\right\|} \]

取整函数

\left \lfloor \frac{a}{b} \right \rfloor

\[{\displaystyle \left\lfloor {\frac {a}{b}}\right\rfloor } \]

取顶函数

\left \lceil \frac{c}{d} \right \rceil

\[{\displaystyle \left\lceil {\frac {c}{d}}\right\rceil } \]

斜线与反斜线

\left / \frac{a}{b} \right \backslash

\[{\displaystyle \left/{\frac {a}{b}}\right\backslash } \]

上下箭头

\left \uparrow \frac{a}{b} \right \downarrow

\[{\displaystyle \left\uparrow {\frac {a}{b}}\right\downarrow } \]

\left \Uparrow \frac{a}{b} \right \Downarrow

\[{\displaystyle \left\Uparrow {\frac {a}{b}}\right\Downarrow } \]

\left \updownarrow \frac{a}{b} \right \Updownarrow

\[{\displaystyle \left\updownarrow {\frac {a}{b}}\right\Updownarrow } \]

混合括号

\left[ 0,1 \right)

\[{\displaystyle \left[0,1\right)} \]

\left \langle \psi \right |

\(\left \langle \psi \right |\)

如果括号只有一边，要用 \left. 或 \right. 匹配另一边。

单左括号

\left \{\frac{a}{b} \right.

\[{\displaystyle \left\{{\frac {a}{b}}\right.} \]

单右括号

\left. \frac{a}{b} \right \}

\[{\displaystyle \left.{\frac {a}{b}}\right\}} \]

备注：

  • 可以使用 \big, \Big, \bigg, \Bigg 控制括号的大小，比如代码

    \Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg )

    显示︰

    \[\Bigg ( \bigg [ \Big \{ \big \langle \left | \| \frac{a}{b} \| \right | \big \rangle \Big \} \bigg ] \Bigg ) \]

空格

注意 TeX 能够自动处理大多数的空格，但是您有时候需要自己来控制。

功能|语法|显示|宽度

2 个 quad 空格

\alpha\qquad\beta

\[{\displaystyle \alpha \qquad \beta} \]

\[{\displaystyle mm} \]

quad 空格

\alpha\quad\beta

\[{\displaystyle \alpha \quad \beta} \]

\[{\displaystyle m} \]

大空格

\alpha\ \beta

\[{\displaystyle \alpha \ \beta} \]

\[{\displaystyle {\frac{m}{3}}} \]

中等空格

\alpha\;\beta

\[{\displaystyle \alpha \;\beta} \]

\[{\displaystyle {\frac {2m}{7}}} \]

小空格

\alpha\,\beta

\[{\displaystyle \alpha \,\beta} \]

\[{\displaystyle {\frac {m}{6}}} \]

没有空格

\alpha\beta

\[{\displaystyle \alpha \beta } \]

\[{\displaystyle 0} \]

紧贴

\alpha\!\beta

\[{\displaystyle \alpha \!\beta} \]

\[{\displaystyle -{\frac {m}{6}}} \]

颜色

Cmd Markdown 公式指导手册里是这样写的：

使用 \color{颜色}{文字} 来更改特定的文字颜色。
更改文字颜色 需要浏览器支持 ，如果浏览器不知道你所需的颜色，那么文字将被渲染为黑色。

对于较旧的浏览器（HTML4与CSS2），以下颜色是被支持的：

输入 显示 输入 显示
black \(\color{black}{text}\) grey \(\color{grey}{text}\)
silver \(\color{silver}{text}\) white \(\color{white}{text}\)
maroon \(\color{maroon}{text}\) red \(\color{red}{text}\)
yellow \(\color{yellow}{text}\) lime \(\color{lime}{text}\)
olive \(\color{olive}{text}\) green \(\color{green}{text}\)
teal \(\color{teal}{text}\) auqa \(\color{auqa}{text}\)
blue \(\color{blue}{text}\) navy \(\color{navy}{text}\)
purple \(\color{purple}{text}\) fuchsia \(\color{fuchsia}{text}\)

对于较新的浏览器（HTML5与CSS3），额外的124种颜色将被支持：

输入 \color {#rgb} {text} 来自定义更多的颜色，其中 #rgb 的 r g b 可输入 0-9 和 a-f 来表示红色、绿色和蓝色的纯度（饱和度）。

  • 例子：
\begin{array}{|rrrrrrrr|}\hline
\verb+#000+ & \color{#000}{text} & & &
\verb+#00F+ & \color{#00F}{text} & & \\
& & \verb+#0F0+ & \color{#0F0}{text} &
& & \verb+#0FF+ & \color{#0FF}{text}\\
\verb+#F00+ & \color{#F00}{text} & & &
\verb+#F0F+ & \color{#F0F}{text} & & \\
& & \verb+#FF0+ & \color{#FF0}{text} &
& & \verb+#FFF+ & \color{#FFF}{text}\\
\hline
\end{array}
  • 显示：

\[\begin{array}{|rrrrrrrr|}\hline \verb+#000+ & \color{#000}{text} & & & \verb+#00F+ & \color{#00F}{text} & & \\ & & \verb+#0F0+ & \color{#0F0}{text} & & & \verb+#0FF+ & \color{#0FF}{text}\\ \verb+#F00+ & \color{#F00}{text} & & & \verb+#F0F+ & \color{#F0F}{text} & & \\ & & \verb+#FF0+ & \color{#FF0}{text} & & & \verb+#FFF+ & \color{#FFF}{text}\\ \hline \end{array} \]

  • 例子：
\begin{array}{|rrrrrrrr|}
\hline
\verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text}  \\
\verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text}  \\
\verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text}  \\
\verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text}  \\
\hline
\verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text}  \\
\verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text}  \\
\verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text}  \\
\verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text}  \\
\hline
\verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text}  \\
\verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text}  \\
\verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text}  \\
\verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text}  \\
\hline
\end{array}
  • 显示：

\[\begin{array}{|rrrrrrrr|} \hline \verb+#000+ & \color{#000}{text} & \verb+#005+ & \color{#005}{text} & \verb+#00A+ & \color{#00A}{text} & \verb+#00F+ & \color{#00F}{text} \\ \verb+#500+ & \color{#500}{text} & \verb+#505+ & \color{#505}{text} & \verb+#50A+ & \color{#50A}{text} & \verb+#50F+ & \color{#50F}{text} \\ \verb+#A00+ & \color{#A00}{text} & \verb+#A05+ & \color{#A05}{text} & \verb+#A0A+ & \color{#A0A}{text} & \verb+#A0F+ & \color{#A0F}{text} \\ \verb+#F00+ & \color{#F00}{text} & \verb+#F05+ & \color{#F05}{text} & \verb+#F0A+ & \color{#F0A}{text} & \verb+#F0F+ & \color{#F0F}{text} \\ \hline \verb+#080+ & \color{#080}{text} & \verb+#085+ & \color{#085}{text} & \verb+#08A+ & \color{#08A}{text} & \verb+#08F+ & \color{#08F}{text} \\ \verb+#580+ & \color{#580}{text} & \verb+#585+ & \color{#585}{text} & \verb+#58A+ & \color{#58A}{text} & \verb+#58F+ & \color{#58F}{text} \\ \verb+#A80+ & \color{#A80}{text} & \verb+#A85+ & \color{#A85}{text} & \verb+#A8A+ & \color{#A8A}{text} & \verb+#A8F+ & \color{#A8F}{text} \\ \verb+#F80+ & \color{#F80}{text} & \verb+#F85+ & \color{#F85}{text} & \verb+#F8A+ & \color{#F8A}{text} & \verb+#F8F+ & \color{#F8F}{text} \\ \hline \verb+#0F0+ & \color{#0F0}{text} & \verb+#0F5+ & \color{#0F5}{text} & \verb+#0FA+ & \color{#0FA}{text} & \verb+#0FF+ & \color{#0FF}{text} \\ \verb+#5F0+ & \color{#5F0}{text} & \verb+#5F5+ & \color{#5F5}{text} & \verb+#5FA+ & \color{#5FA}{text} & \verb+#5FF+ & \color{#5FF}{text} \\ \verb+#AF0+ & \color{#AF0}{text} & \verb+#AF5+ & \color{#AF5}{text} & \verb+#AFA+ & \color{#AFA}{text} & \verb+#AFF+ & \color{#AFF}{text} \\ \verb+#FF0+ & \color{#FF0}{text} & \verb+#FF5+ & \color{#FF5}{text} & \verb+#FFA+ & \color{#FFA}{text} & \verb+#FFF+ & \color{#FFF}{text} \\ \hline \end{array} \]

*的数学公式教程里是这样写的：

语法：{\color{颜色}表达式}

作者实测：在部分浏览器中，上面的语法可能是错误的（只将表达式的第一个字符着色），\color{颜色}{文字}的语法才是正确的。例如：

{\color{Red}abc}显示$${\color{Red}abc}$$
\color{Red}{abc}显示\(\color{Red}{abc}\)

支持色调表：

\[{\displaystyle \color {Apricot}{\text{Apricot}}} \]

\[{\displaystyle \color {Aquamarine}{\text{Aquamarine}}} \]

\[{\displaystyle \color {Bittersweet}{\text{Bittersweet}}} \]

\[{\displaystyle \color {Black}{\text{Black}}} \]

\[{\displaystyle \color {Blue}{\text{Blue}}} \]

\[{\displaystyle \color {BlueGreen}{\text{BlueGreen}}} \]

\[{\displaystyle \color {BlueViolet}{\text{BlueViolet}}} \]

\[{\displaystyle \color {BrickRed}{\text{BrickRed}}} \]

\[{\displaystyle \color {Brown}{\text{Brown}}} \]

\[{\displaystyle \color {BurntOrange}{\text{BurntOrange}}} \]

\[{\displaystyle \color {CadetBlue}{\text{CadetBlue}}} \]

\[{\displaystyle \color {CarnationPink}{\text{CarnationPink}}} \]

\[{\displaystyle \color {Cerulean}{\text{Cerulean}}} \]

\[{\displaystyle \color {CornflowerBlue}{\text{CornflowerBlue}}} \]

\[{\displaystyle \color {Cyan}{\text{Cyan}}} \]

\[{\displaystyle \color {Dandelion}{\text{Dandelion}}} \]

\[{\displaystyle \color {DarkOrchid}{\text{DarkOrchid}}} \]

\[{\displaystyle \color {Emerald}{\text{Emerald}}} \]

\[{\displaystyle \color {ForestGreen}{\text{ForestGreen}}} \]

\[{\displaystyle \color {Fuchsia}{\text{Fuchsia}}} \]

\[{\displaystyle \color {Goldenrod}{\text{Goldenrod}}} \]

\[{\displaystyle \color {Gray}{\text{Gray}}} \]

\[{\displaystyle \color {Green}{\text{Green}}} \]

\[{\displaystyle \color {GreenYellow}{\text{GreenYellow}}} \]

\[{\displaystyle \color {JungleGreen}{\text{JungleGreen}}} \]

\[{\displaystyle \color {Lavender}{\text{Lavender}}} \]

\[{\displaystyle \color {LimeGreen}{\text{LimeGreen}}} \]

\[{\displaystyle \color {Magenta}{\text{Magenta}}} \]

\[{\displaystyle \color {Mahogany}{\text{Mahogany}}} \]

\[{\displaystyle \color {Maroon}{\text{Maroon}}} \]

\[{\displaystyle \color {Melon}{\text{Melon}}} \]

\[{\displaystyle \color {MidnightBlue}{\text{MidnightBlue}}} \]

\[{\displaystyle \color {Mulberry}{\text{Mulberry}}} \]

\[{\displaystyle \color {NavyBlue}{\text{NavyBlue}}} \]

\[{\displaystyle \color {OliveGreen}{\text{OliveGreen}}} \]

\[{\displaystyle \color {Orange}{\text{Orange}}} \]

\[{\displaystyle \color {OrangeRed}{\text{OrangeRed}}} \]

\[{\displaystyle \color {Orchid}{\text{Orchid}}} \]

\[{\displaystyle \color {Peach}{\text{Peach}}} \]

\[{\displaystyle \color {Periwinkle}{\text{Periwinkle}}} \]

\[{\displaystyle \color {PineGreen}{\text{PineGreen}}} \]

\[{\displaystyle \color {Plum}{\text{Plum}}} \]

\[{\displaystyle \color {ProcessBlue}{\text{ProcessBlue}}} \]

\[{\displaystyle \color {Purple}{\text{Purple}}} \]

\[{\displaystyle \color {RawSienna}{\text{RawSienna}}} \]

\[{\displaystyle \color {Red}{\text{Red}}} \]

\[{\displaystyle \color {RedOrange}{\text{RedOrange}}} \]

\[{\displaystyle \color {RedViolet}{\text{RedViolet}}} \]

\[{\displaystyle \color {Rhodamine}{\text{Rhodamine}}} \]

\[{\displaystyle \color {RoyalBlue}{\text{RoyalBlue}}} \]

\[{\displaystyle \color {RoyalPurple}{\text{RoyalPurple}}} \]

\[{\displaystyle \color {RubineRed}{\text{RubineRed}}} \]

\[{\displaystyle \color {Salmon}{\text{Salmon}}} \]

\[{\displaystyle \color {SeaGreen}{\text{SeaGreen}}} \]

\[{\displaystyle \color {Sepia}{\text{Sepia}}} \]

\[{\displaystyle \color {SkyBlue}{\text{SkyBlue}}} \]

\[{\displaystyle \color {SpringGreen}{\text{SpringGreen}}} \]

\[{\displaystyle \color {Tan}{\text{Tan}}} \]

\[{\displaystyle \color {TealBlue}{\text{TealBlue}}} \]

\[{\displaystyle \color {Thistle}{\text{Thistle}}} \]

\[{\displaystyle \color {Turquoise}{\text{Turquoise}}} \]

\[{\displaystyle \color {Violet}{\text{Violet}}} \]

\[{\displaystyle \color {VioletRed}{\text{VioletRed}}} \]

\[{\displaystyle \color {White}{\text{White}}} \]

\[{\displaystyle \color {WildStrawberry}{\text{WildStrawberry}}} \]

\[{\displaystyle \color {Yellow}{\text{Yellow}}} \]

\[{\displaystyle \color {YellowGreen}{\text{YellowGreen}}} \]

\[{\displaystyle \color {YellowOrange}{\text{YellowOrange}}} \]

＊注︰输入时第一个字母必需以大写输入，如\color{OliveGreen}。

例子

  • {\color{Blue}x^2}+{\color{Brown}2x} - {\color{OliveGreen}1}

    \[{\displaystyle {\color {Blue}x^{2}}+{\color {Brown}2x}-{\color {OliveGreen}1}} \]

  • x_{\color{Maroon}1,2}=\frac{-b\pm\sqrt{{\color{Maroon}b^2-4ac}}}{2a}

    \[{\displaystyle x_{\color {Maroon}1,2}={\frac {-b\pm {\sqrt {\color {Maroon}b^{2}-4ac}}}{2a}}} \]

外部链接

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