参考*的数学公式教程
参考Cmd Markdown 公式指导手册
通过使用 \(\LaTeX\) 的变体和
这里所使用的 LaTeX 版本是 AMS-LaTeX 语言的有限的一部分得到支持。
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
\({\displaystyle \lim u,\liminf v,\limsup w}\)
\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
\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
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}
\({\displaystyle {\vec {c}}}\)
\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
\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
\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\, \mathrm{d}x
\({\displaystyle \int _{-N}^{N}e^{x}\,\mathrm {d} x}\)
\begin{matrix} \int_{-N}^{N} e^x\, \mathrm{d}x \end{matrix}
\({\displaystyle {\begin{matrix}\int _{-N}^{N}e^{x}\,\mathrm {d} x\end{matrix}}}\)
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、矩阵和多行列式
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
\({\displaystyle {\tfrac {2}{4}}=0.5}\)
大型分数（嵌套）
\cfrac{2}{c + \cfrac{2}{d + \cfrac{2}{4}}} = a
\({\displaystyle {\cfrac {2}{c+{\cfrac {2}{d+{\cfrac {2}{4}}}}}}=a}\)
大型分数（不嵌套）
\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}
\({\displaystyle {\binom {n}{r}}={\dbinom {n}{n-r}}=\mathrm {C} _{n}^{r}=\mathrm {C} _{n}^{n-r}}\)
矩阵
\begin{matrix}
x & y \\
z & v
\end{matrix}\({\displaystyle {\begin{matrix}x&y\\z&v\end{matrix}}}\)
\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}\({\displaystyle {\begin{Vmatrix}x&y\\z&v\end{Vmatrix}}}\)
\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}\({\displaystyle {\begin{pmatrix}x&y\\z&v\end{pmatrix}}}\)
条件定义
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
\begin{align}
f(x) & = (m+n)^2 \\
& = m^2+2mn+n^2 \\
\end{align}
\({\displaystyle {\begin{aligned}f(x)&=(m+n)^{2}\\&=m^{2}+2mn+n^{2}\\\end{aligned}}}\)
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}\({\displaystyle {\begin{aligned}3^{6n+3}+4^{6n+3}&\equiv (3^{3})^{2n+1}+(4^{3})^{2n+1}\\&\equiv 27^{2n+1}+64^{2n+1}\\&\equiv 27^{2n+1}+(-27)^{2n+1}\\&\equiv 27^{2n+1}-27^{2n+1}\\&\equiv 0{\pmod {91}}\\\end{aligned}}}\)
\begin{alignat}{3}
f(x) & = (m-n)^2 \\
f(x) & = (-m+n)^2 \\
& = m^2-2mn+n^2 \\
\end{alignat}\({\displaystyle {\begin{alignedat}{3}f(x)&=(m-n)^{2}\\f(x)&=(-m+n)^{2}\\&=m^{2}-2mn+n^{2}\\\end{alignedat}}}\)
多行等式（左对齐）
\begin{array}{lcl}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}\({\displaystyle {\begin{array}{lcl}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}\)
多行等式（右对齐）
\begin{array}{lcr}
z & = & a \\
f(x,y,z) & = & x + y + z
\end{array}\({\displaystyle {\begin{array}{lcr}z&=&a\\f(x,y,z)&=&x+y+z\end{array}}}\)
方程组
\begin{cases}
3x + 5y + z \\
7x - 2y + 4z \\
-6x + 3y + 2z
\end{cases}\({\displaystyle {\begin{cases}3x+5y+z\\7x-2y+4z\\-6x+3y+2z\end{cases}}}\)
数组
\begin{array}{ccc}
a & b & S \\
\hline
0&0&1\\
0&1&1\\
1&0&1\\
1&1&0\\
\end{array}\({\displaystyle {\begin{array}{ccc}a&b&S\\\hline 0&0&1\\0&1&1\\1&0&1\\1&1&0\\\end{array}}}\)
字体
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
\({\displaystyle \rho \sigma \tau \upsilon \phi \chi \psi \omega}\)
\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
\({\displaystyle \aleph \beth \gimel \daleth}\)
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}
\({\displaystyle {\text{if}}~n\ {\text{is even}}}\)
括号
功能|语法|显示
短括号
\frac{1}{2}
\({\displaystyle ({\frac {1}{2}})}\)
长括号
\left(\frac{1}{2} \right
\({\displaystyle \left({\frac {1}{2}}\right)}\)
您可以使用 \left 和 \right 来显示不同的括号：
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 |
\(\left \langle \psi \right |\)
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
语法
- 字体颜色︰
{\color{色调}表达式}
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
一个介绍 \(\TeX\) 的 PDF 文档（英文）： http://www.ctan.org/tex-archive/info/gentle/gentle.pdf
手画符号搜索 \(\LaTeX\) 代码: http://detexify.kirelabs.org/classify.html