在论文和博客的写作中,经常会用到Latex的语法来书写数学公式,一份详细的数学符号对照表必不可少,本文重写了部分 Markdown 公式指导手册 。
-1.求和积分的上下标位置
\sum\nolimits_{j=1}^{M} 上下标位于求和符号的水平右端,
\sum\limits_{j=1}^{M} 上下标位于求和符号的上下处,
\sum_{j=1}^{M} 对上下标位置没有设定,会随公式所处环境自动调整。
\[\sum\nolimits_{j=1}^{M}\\
\sum\limits_{j=1}^{M}\\
\sum_{j=1}^{M}
\]
0.大括号公式和一般括号
大括号显示
\left\{
\begin{array}{**lr**}
x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\
y=s, & 0\leq s\leq L,|t|\leq1.\\
z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), &
\end{array}
\right.
\[\left\{
\begin{array}{**lr**}
x=\dfrac{3\pi}{2}(1+2t)\cos(\dfrac{3\pi}{2}(1+2t)), & \\
y=s, & 0\leq s\leq L,|t|\leq1.\\
z=\dfrac{3\pi}{2}(1+2t)\sin(\dfrac{3\pi}{2}(1+2t)), &
\end{array}
\right.
\]
F^{HLLC}=\left\{
\begin{array}{rcl}
F_L & & {0 < S_L}\\
F^*_L & & {S_L \leq 0 < S_M}\\
F^*_R & & {S_M \leq 0 < S_R}\\
F_R & & {S_R \leq 0}
\end{array} \right.
\[F^{HLLC}=\left\{
\begin{array}{rcl}
F_L & & {0 < S_L}\\
F^*_L & & {S_L \leq 0 < S_M}\\
F^*_R & & {S_M \leq 0 < S_R}\\
F_R & & {S_R \leq 0}
\end{array} \right.
\]
1.常用公式
描述 |
写法 |
效果展示 |
---|
上下标 |
a_1 / e_x |
\(a_1/e_x\) |
平方根 |
\sqrt{x} |
\(\sqrt{x}\) |
上下方水平线 |
\overline{m+n} / \underline{m+n} |
\(\overline{m+n} /\underline{m+n}\) |
上下方大括号 |
\overbrace{m+n} / \underbrace{m+n} |
\(\overbrace{m+n} / \underbrace{m+n}\) |
向量 |
\vec a |
\(\vec a\) |
分数 |
\frac{1}{2} |
\(\frac{1}{2}\) |
求和 |
\sum_{i=1}^n |
\(\sum_{i=1}^n\) |
积分 |
\int_0^{\pi/2} |
\(\int_0^{\pi/2}\) |
累乘 |
\prod_\epsilon |
\(\prod_\epsilon\) |
优化 |
\mathop{\arg\min}_{\theta} |
\(\mathop{\arg\min}_{\theta}\) |
时间复杂度 |
\mathcal{O}(1) |
\(\mathcal{O}(1)\) |
1.1 大尺度运算符
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\sum\) |
\sum |
\(\bigcup\) |
\bigcup |
\(\bigvee\) |
\bigvee |
\(\bigoplus\) |
\bigoplus |
\(\prod\) |
\prod |
\(\bigcap\) |
\bigcap |
\(\bigwedge\) |
\bigwedge |
\(\bigotimes\) |
\bigotimes |
\(\coprod\) |
\coprod |
\(\bigsqcup\) |
\bigsqcup |
|
|
\(\bigodot\) |
\bigodot |
\(\int\) |
\int |
\(\oint\) |
\oint |
|
|
\(\biguplus\) |
\biguplus |
另外 \overline
能覆盖所有括号中的文本,\bar
长度只能覆盖一个字母。
$\overline{\bigcup A_i} = \bigcap \overline A_i$
\[\overline{\bigcup A_i} = \bigcap \overline A_i
\]
1.2 矩阵
需要 amsmath
宏包:
\[ \begin{pmatrix} a&b\\c&d \end{pmatrix} \quad
\begin{bmatrix} a&b\\c&d \end{bmatrix} \quad
\begin{Bmatrix} a&b\\c&d \end{Bmatrix} \quad
\begin{vmatrix} a&b\\c&d \end{vmatrix} \quad
\begin{Vmatrix} a&b\\c&d \end{Vmatrix} \]
\[\begin{pmatrix} a&b\\c&d \end{pmatrix} \quad
\begin{bmatrix} a&b\\c&d \end{bmatrix} \quad
\begin{Bmatrix} a&b\\c&d \end{Bmatrix} \quad
\begin{vmatrix} a&b\\c&d \end{vmatrix} \quad
\begin{Vmatrix} a&b\\c&d \end{Vmatrix}
\]
使用 smallmatrix
环境,可以生成行内公式的小矩阵:
Marry has a little matrix $ ( \begin{smallmatrix} a&b\\ c&d \end{smallmatrix} )$
Marry has a little matrix $ ( \begin{smallmatrix} a&b\ c&d \end{smallmatrix} )$
1.3 括号
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\((\) |
( |
\()\) |
) |
\(\uparrow\) |
\uparrow |
\(\Uparrow\) |
\Uparrow |
\(\lbrack\) |
\[ or \lbrack |
\(\rbrack\) |
\] or \rbrack |
\(\downarrow\) |
\downarrow |
\(\Downarrow\) |
\Downarrow |
\(\\\{\) |
\{ or \lbrace |
\(\}\) |
\} or \rbrace |
\(\updownarrow\) |
\updownarrow |
\(\Updownarrow\) |
\Updownarrow |
\(\langle\) |
\langle |
\(\rangle\) |
\rangle |
$ |
$ |
| or \vert |
\(\parallel\) |
\(\lfloor\) |
\lfloor |
\(\rfloor\) |
\rfloor |
\(\lceil\) |
\lceil |
\(\rceil\) |
\rceil |
\(/\) |
/ |
\(\backslash\) |
\backslash |
\(\lmoustache\) |
\lmoustache |
\(\rmoustache\) |
\rmoustache |
\(\lgroup\) |
\lgroup |
\(\rgroup\) |
\rgroup |
\(\bracevert\) |
\bracevert |
|
|
\(\arrowvert\) |
\arrowvert |
\(\Arrowvert\) |
\Arrowvert |
|
|
|
|
- 不同大小的括号
\Bigg ( \bigg [ \Big \{\big \langle \left \vert \parallel \frac{a}{b} \parallel \right \vert \big \rangle \Big \} \bigg ] \Bigg )
:
\[\Bigg ( \bigg [ \Big \{\big \langle \left \vert \parallel \frac{a}{b} \parallel \right \vert \big \rangle \Big \} \bigg ] \Bigg ):
\]
- 自适应大小的括号
\left( \frac{a}{b} \right)
:
\[\left( \frac{a}{b} \right)
\]
- 单边括号
\left . \frac{a}{b} \right \rbrace
:
\[\left . \frac{a}{b} \right \rbrace
\]
- 混合括号
\left \langle \psi \right \vert
:
\[\left \langle \psi \right \vert
\]
1.4 空格
LaTex 在数学公式中的字符间隔是默认自动调整的,直接输入空格会被忽略掉,当我们需要自定义字母间隔时,需要手动输入空格:
空格 |
写法 |
显示 |
备注 |
---|
两个quad空格 |
a \qquad b |
\(a \qquad b\) |
两个m的宽度 |
quad空格 |
a \quad b |
\(a \quad b\) |
一个m的宽度 |
大空格 |
a\ b |
\(a\ b\) |
1/3m宽度 |
中等空格 |
a;b |
\(a\;b\) |
2/7m宽度 |
小空格 |
a,b |
\(a\,b\) |
1/6m宽度 |
没有空格 |
ab |
\(ab\) |
|
紧贴 |
a!b |
\(a!b\) |
缩进1/6m宽度 |
2. 重音符
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\hat{a}\) |
\hat{a} |
\(\check{a}\) |
\check{a} |
\(\tilde{a}\) |
\tilde{a} |
\(\acute{a}\) |
\acute{a} |
\(\grave{a}\) |
\grave{a} |
\(\dot{a}\) |
\dot{a} |
\(\ddot{a}\) |
\ddot{a} |
\(\breve{a}\) |
\breve{a} |
\(\bar{a}\) |
\bar{a} |
\(\vec{a}\) |
\vec{a} |
\(\widehat{A}\) |
\widehat{A} |
\(\widetilde{A}\) |
\widetilde{A} |
3. 希腊字母
3.1 小写希腊字母
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\alpha\) |
\alpha |
\(\theta\) |
\theta |
\(o\) |
o |
\(\upsilon\) |
\upsilon |
\(\beta\) |
\beta |
\(\vartheta\) |
\vartheta |
\(\pi\) |
\pi |
\(\phi\) |
\phi |
\(\gamma\) |
\gamma |
\(\iota\) |
\iota |
\(\varpi\) |
\varpi |
\(\varphi\) |
\varphi |
\(\delta\) |
\delta |
\(\kappa\) |
\kappa |
\(\rho\) |
\rho |
\(\chi\) |
\chi |
\(\epsilon\) |
\epsilon |
\(\lambda\) |
\lambda |
\(\varrho\) |
\varrho |
\(\psi\) |
\psi |
\(\varepsilon\) |
\varepsilon |
\(\mu\) |
\mu |
\(\sigma\) |
\sigma |
\(\omega\) |
\omega |
\(\zeta\) |
\zeta |
\(\nu\) |
\nu |
\(\varsigma\) |
\varsigma |
|
|
\(\eta\) |
\eta |
\(\xi\) |
\xi |
\(\tau\) |
\tau |
|
|
3.2 大写希腊字母
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\Gamma\) |
\Gamma |
\(\Lambda\) |
\Lambda |
\(\Sigma\) |
\Sigma |
\(\Psi\) |
\Psi |
\(\Delta\) |
\Delta |
\(\Xi\) |
\Xi |
\(\Upsilon\) |
\Upsilon |
\(\Omega\) |
\Omega |
\(\Theta\) |
\Theta |
\(\Pi\) |
\Pi |
\(\Phi\) |
\Phi |
|
|
4. 二元符号
4.1 二元关系符
可以在下述的命令中加上 \not 来得到
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(<\) |
< |
\(>\) |
> |
\(=\) |
= |
\(\le\) |
\leq or \le |
\(\ge\) |
\geq or \ge |
\(\equiv\) |
\equiv |
\(\ll\) |
\ll |
\(\gg\) |
\gg |
\(\doteq\) |
\doteq |
\(\prec\) |
\prec |
\(\succ\) |
\succ |
\(\sim\) |
\sim |
\(\preceq\) |
\preceq |
\(\succeq\) |
\succeq |
\(\simeq\) |
\simeq |
\(\approx\) |
\approx |
\(\subset\) |
\subset |
\(\supset\) |
\supset |
\(\subseteq\) |
\subseteq |
\(\supseteq\) |
\supseteq |
\(\sqsubset\) |
\sqsubset |
\(\sqsupset\) |
\sqsupset |
\(\sqsubseteq\) |
\sqsubseteq |
\(\sqsupseteq\) |
\sqsupseteq |
\(\cong\) |
\cong |
\(\Join\) |
\Join |
\(\bowtie\) |
\bowtie |
\(\propto\) |
\propto |
\(\in\) |
\in |
\(\ni\) |
\ni or \owns |
\(\vdash\) |
\vdash |
\(\dashv\) |
\dashv |
\(\models\) |
\models |
\(\mid\) |
\mid |
\(\parallel\) |
\parallel |
\(\perp\) |
\perp |
\(\smile\) |
\smile |
\(\frown\) |
\frown |
\(\asymp\) |
\asymp |
\(:\) |
: |
\(\notin\) |
\notin |
\(\ne\) |
\neq or \ne |
|
|
|
|
4.2 二元运算符
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(+\) |
+ |
\(-\) |
- |
\(\times\) |
\times |
\(\div\) |
\div |
\(\pm\) |
\pm |
\(\mp\) |
\mp |
\(\triangleleft\) |
\triangleleft |
\(\triangleright\) |
\triangleright |
\(\cdot\) |
\cdot |
\(\setminus\) |
\setminus |
\(\star\) |
\star |
\(\ast\) |
\ast |
\(\cup\) |
\cup |
\(\cap\) |
\cap |
\(\sqcup\) |
\sqcup |
\(\sqcap\) |
\sqcap |
\(\lor\) |
\vee or \lor |
\(\land\) |
\wedge or \land |
\(\circ\) |
\circ |
\(\bullet\) |
\bullet |
\(\oplus\) |
\oplus |
\(\ominus\) |
\ominus |
\(\odot\) |
\odot |
\(\oslash\) |
\oslash |
\(\otimes\) |
\otimes |
\(\bigcirc\) |
\bigcirc |
\(\diamond\) |
\diamond |
\(\uplus\) |
\uplus |
\(\bigtriangleup\) |
\bigtriangleup |
\(\bigtriangledown\) |
\bigtriangledown |
\(\lhd\) |
\lhd |
\(\rhd\) |
\rhd |
\(\unlhd\) |
\unlhd |
\(\unrhd\) |
\unrhd |
\(\amalg\) |
\amalg |
\(\wr\) |
\wr |
\(\dagger\) |
\dagger |
\(\ddagger\) |
\ddagger |
|
|
|
|
5. 箭头
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\gets\) |
\leftarrow or \gets |
\(\to\) |
\rightarrow or \to |
\(\longleftarrow\) |
\longleftarrow |
\(\longrightarrow\) |
\longrightarrow |
\(\uparrow\) |
\uparrow |
\(\downarrow\) |
\downarrow |
\(\updownarrow\) |
\updownarrow |
\(\leftrightarrow\) |
\leftrightarrow |
\(\Uparrow\) |
\Uparrow |
\(\Downarrow\) |
\Downarrow |
\(\Updownarrow\) |
\Updownarrow |
\(\longleftrightarrow\) |
\longleftrightarrow |
\(\Leftarrow\) |
\Leftarrow |
\(\Longleftarrow\) |
\Longleftarrow |
\(\Rightarrow\) |
\Rightarrow |
\(\Longrightarrow\) |
\Longrightarrow |
\(\Leftrightarrow\) |
\Leftrightarrow |
\(\Longleftrightarrow\) |
\Longleftrightarrow |
\(\mapsto\) |
\mapsto |
\(\longmapsto\) |
\longmapsto |
\(\nearrow\) |
\nearrow |
\(\searrow\) |
\searrow |
\(\swarrow\) |
\swarrow |
\(\nwarrow\) |
\nwarrow |
\(\hookleftarrow\) |
\hookleftarrow |
\(\hookrightarrow\) |
\hookrightarrow |
\(\rightleftharpoons\) |
\rightleftharpoons |
\(\iff\) |
\iff |
\(\leftharpoonup\) |
\leftharpoonup |
\(\rightharpoonup\) |
\rightharpoonup |
\(\leftharpoondown\) |
\leftharpoondown |
\(\rightharpoondown\) |
\rightharpoondown |
\(\leadsto\) |
\leadsto |
|
|
|
|
|
|
6. 其他符号
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\dots\) |
\dots |
\(\cdots\) |
\cdots |
\(\vdots\) |
\vdots |
\(\ddots\) |
\ddots |
\(\hbar\) |
\hbar |
\(\imath\) |
\imath |
\(\jmath\) |
\jmath |
\(\ell\) |
\ell |
\(\Re\) |
\Re |
\(\Im\) |
\Im |
\(\aleph\) |
\aleph |
\(\wp\) |
\wp |
\(\forall\) |
\forall |
\(\exists\) |
\exists |
\(\mho\) |
\mho |
\(\partial\) |
\partial |
\(’\) |
’ |
\(\prime\) |
\prime |
\(\emptyset\) |
\emptyset |
\(\infty\) |
\infty |
\(\nabla\) |
\nabla |
\(\triangle\) |
\triangle |
\(\Box\) |
\Box |
\(\Diamond\) |
\Diamond |
\(\bot\) |
\bot |
\(\top\) |
\top |
\(\angle\) |
\angle |
\(\surd\) |
\surd |
\(\diamondsuit\) |
\diamondsuit |
\(\heartsuit\) |
\heartsuit |
\(\clubsuit\) |
\clubsuit |
\(\spadesuit\) |
\spadesuit |
\(\lnot\) |
\neg or \lnot |
\(\flat\) |
\flat |
\(\natural\) |
\natural |
\(\sharp\) |
\sharp |
7.其他
符号 |
写法 |
符号 |
写法 |
符号 |
写法 |
---|
\(\\S\) |
\S |
\(\\P\) |
\P |
|
|
字体 |
写法 |
---|
\(\mathbb{R}\) |
\mathbb{R} |
\(mathcal{L}\) |
\mathcal{L} |
PS: 原文中还有其他符号(如AMS运算符,希伯来字母等),但MathJax中或是不支持,或是使用频率太低,故而在这里不再写入
参考
[1] 常用数学符号的 LaTeX 表示方法
[2] LaTeX Notes 雷太赫排版系统简介 v2.56 包太雷
[3] LaTeX数学符号公式汇总