整理Markdown 公式编辑常用数学符号

样式

公式位置

行内模式式使用$...$,在文本之间插入公式;显示模式$$...$$,在单独的一行使用。

上标、下标

上标: ^,下标:_
示例: C_n^2\(C_n^2\)
前置上下标{}_1^2\!X_3^4\({}_1^2\!C_3^4\)

分组

把相同等级的表达式放到一起。
符号: {}
e^{10}显示为\(e^{10}\),而e^10则为\(e^10\)

字体样式

显示 符号 字体
\(ABCabc\) $ABCabc$ 直接写
\(\text{ABCabc}\) \text{ABCabc} 文本格式(内部可以再使用`$
--------------------- --------------------------------- ------------------------------
\(\mathbf{ABCabc}\) \mathbf{ABCabc} 加粗
\(\boldsymbol{\alpha}\) \boldsymbol{\alpha} 加粗(其它字符)
\(\mathit{ABCabc}\) \mathit{ABCabc} 斜体
\(\pmb{ABCabc}\) \pmb{ABCabc} 粗斜体
\(\mathbb{ABCabc}\) \mathbb{ABCabc}\Bbb{ABCabc} blackboard bold font
\(\mathtt{ABCabc}\) \mathtt{ABCabc} typewriter font
\(\mathrm{ABCabc}\) \mathrm{ABCabc} roman font
\(\mathsf{ABCabc}\) \mathsf{ABCabc} sans-serif font
\(\mathcal{ABCabc}\) \mathcal{ABCabc} calligraphic letters
\(\mathscr{ABCabc}\) \mathscr{ABCabc} script letters
\(\mathfrak{ABCabc}\) \mathfrak{ABCabc} Frakur letters

字体大小

显示 符号
\(ABCabc\) ABCabc
\(\tiny ABCabc\) \tiny ABCabc
\(\small ABCabc\) \small ABCabc
\(\normalsize ABCabc\) \normalsize ABCabc
\(\large ABCabc\) \large ABCabc
\(\Large ABCabc\) \Large ABCabc
\(\huge ABCabc\) \huge ABCabc
\(\Huge ABCabc\) \Huge ABCabc

使用分组的方式来控制不同字体的大小,如ABC {\tiny ABC} {\large ABC}显示为\(ABC {\tiny ABC} {\large ABC}\)

希腊字母

小写 符号 大写 符号 小写 符号 大写 符号
\(\alpha\) \alpha \(\Alpha\) \Alpha \(\beta\) \beta \(\Beta\) \Beta
\(\gamma\) \gamma \(\Gamma\) \Gamma \(\delta\) \delta \(\Delta\) \Delta
\(\epsilon\) \epsilon \(\Epsilon\) \Epsilon \(\zeta\) \zeta \(\Zeta\) \Zeta
\(\eta\) \eta \(\Eta\) \Eta \(\theta\) \theta \(\Theta\) \Theta
\(\iota\) \iota \(\Iota\) \Iota \(\kappa\) \kappa \(\Kappa\) \Kappa
\(\lambda\) \lambda \(\Lambda\) \Lambda \(\mu\) \mu \(\Mu\) \Mu
\(\nu\) \nu \(\Nu\) \Nu \(\xi\) \xi \(\Xi\) \Xi
\(\pi\) \pi \(\Pi\) \Pi \(\rho\) \rho \(\Rho\) \Rho
\(\sigma\) \sigma \(\Sigma\) \Sigma \(\tau\) \tau \(\Tau\) \Tau
\(\upsilon\) \upsilon \(\Upsilon\) \Upsilon \(\phi\) \phi \(\Phi\) \Phi
\(\chi\) \chi \(\Chi\) \Chi \(\psi\) \psi \(\Psi\) \psi
\(\omega\) omega \(\Omega\) \Omega \(\omicron\) \omicron \(\Omicron\) \Omicron

若需要斜体希腊字母,加上前缀var。如\varDelta显示为\(\varDelta\)

算术运算

显示 符号 显示 符号 显示 符号
\(\times\) \times \(\div\) \div \(\cdot\) \cdot
\(<\) < \(>\) > \(\ll\) \ll
\(\gg\) \gg \(\lll\) \lll \(\pm\) \pm
\(\le\) \le\leq \(\ge\) \ge\geq \(\mp\) \mp
\(\leqq\) \leqq \(\geqq\) \geqq \(\neq\) \neq
\(\leqslant\) \leqslant \(\geqslant\) \geqslant \(\approx\) \approx

集合

显示 符号 显示 符号 显示 符号
\(\complement\) \complement \(\in\) \in \(\notin\) \notin
\(\subset\) \subset \(\subseteq\) \subseteq \(\subsetneq\) \subsetneq
\(\cap\) \cap \(\cup\) \cup \(\varnothing\) \varnothing
\(\emptyset\) \emptyset

逻辑运算

显示 符号 显示 符号 显示 符号
\(\land\) \land\wedge \(\lor\) \lor\vee \(\lnot\) \lnot\neg
\(\forall\) \forall \(\exists\) \exists \(\top\) \top
\(\vdash\) \vdash \(\vDash\) \vDash \(\bot\) \bot

括号

括号 符号
\((x)\) (x)
\(\{ x \}\) \{ x \}\lbrace x \rbrace
\([x]\) [x]
\(\vert x\vert\) \vert x \vert
\(\Vert x \Vert\) \Vert x \Vert
\(\langle x \rangle\) \langle x \rangle
\(\lceil x \rceil\) \lceil x \rceil
\(\lfloor x \rfloor\) \lfloor x \rfloor
\(\left(\frac xy \right)\) \left( \frac xy \right)(让括号与公式相适应)
\(\left. \frac 12 \right\}\) \left. \frac 12 \right\}
$ \left{ \frac xy \middle y \neq 0 \right}$
\(\Bigg(\bigg(\Big(\big((x) \big)\Big)\bigg)\Bigg)\) \Bigg(\bigg(\Big(\big((x) \big)\Big)\bigg)\Bigg)
\(\dbinom nr\) \dbinom nr(二项式系数)
\(\binom nr\) \binom nr或者{n \choose r}

空格

显示 命令 说明
\(a b\) a b 无视空格
\(a \qquad b\) a \qquad b
\(a \quad b\) a \quad b
\(a\ b\) a\ b
\(a\;b\) a\;b
\(a\,b\) a\,b
\(a\!b\) a\!b

求和、积分和微分

显示 符号 显示 符号
\(\sum_1^n\) \sum_1^n \(\sum_{i=0}^\infty x^2\) \sum_{i=0}^\infty x^2
\(\int\) \int \(\iint\) \iint
\(\iiint\) \iiint \(\idotsint\) \idotsint
\(\oint\) \oint \(\prod\) \prod
\(\coprod\) \coprod \(\bigcap\) \bigcap
\(\bigcup\) \bigcup \(\bigvee\) \bigvee
\(\bigwedge\) \bigwedge \(\infty\) \infty
\(\nabla\) \nabla \(\partial x\) \partial x
\(\mathrm{d}x\) \mathrm{d}x \(\dot x\) \dot x
\(\ddot y\) \ddot y

分式、根号和函数

显示 符号 说明
\(\frac 12\) \frac 12
\(\dfrac 12\) \dfrac 12 强制分式为显示模式
\(\tfrac 12\) \tfrac 12 强制分式为文本模式
\(\cfrac 12\) \cfrac 12 用于连续分式
\(\frac {x^2}{1+x}\) \frac {x^2}{1+x}
\({x^2 \over 1+x}\) {x^2 \over 1+x} 用于复杂的分式
\(\sqrt{x^3}\) \sqrt{x^3}
\(\sqrt[3]{\frac xy}\) \sqrt[3]{\frac xy}
\(\sin x\) \sin x 大部分可以使用\+ 函数名
\(\operatorname{arcsec}x\) \operatorname{arcsec}x 无标准函数名
\(\lim_{x \to 0}\) \lim_{x \to 0}
\(\varinjlim\) \varinjlim
\(\varprojlim\) \varprojlim
\(\varliminf\) \varliminf
\(\varlimsup\) \varlimsup

箭头符号

显示 符号 显示 符号
\(\Rightarrow\) \Rightarrow \(\Leftarrow\) \Leftarrow
\(a \rightarrow b\) a \rightarrow b \(a \leftarrow b\) a \leftarrow b
\(a \to b\) a \to b(常用) \(a \gets b\) a \gets b(常用)
\(a \Longrightarrow b\) a \Longrightarrow b \(a \Longleftarrow b\) a \Longleftarrow b
\(a \implies b\) a \implies b(常用) \(a \impliedby b\) a \impliedby b(常用)
\(\longrightarrow\) \longrightarrow \(\longleftarrow\) \longleftarrow
\(\Leftrightarrow\) \Leftrightarrow \(\leftrightarrow\) \leftrightarrow
$\Longleftrightarrow $ \Longleftrightarrow\iff \(\longleftrightarrow\) \longleftrightarrow
\(\xrightarrow[y>0]{x+y}\) \xrightarrow[y>0]{x+y} \(\xleftarrow{x+y}\) \xleftarrow{x+y}
\(\longmapsto\) \longmapsto \(\mapsto\) \mapsto
\(\hookleftarrow\) \hookleftarrow \(\hookrightarrow\) \hookrightarrow
\(\searrow\) \searrow \(\nearrow\) nearrow
\(\nwarrow\) \nwarrow \(\swarrow\) swarrow
\(\downarrow\) \downarrow \(\uparrow\) \uparrow
\(\upuparrows\) \upuparrows \(\updownarrow\) \updownarrow
\(\Uparrow\) \Uparrow \(\downdownarrows\) \downdownarrows
\(\Updownarrow\) \Updownarrow \(\Downarrow\) \Downarrow
\(\rightharpoonup\) \rightharpoonup \(\leftharpoonup\) \lefttharpoonup
\(\rightharpoondown\) \rightharpoonup \(\leftharpoondown\) \leftharpoondown
\(\upharpoonleft\) \upharpoonleft \(\downharpoonleft\) \downharpoonleft
\(\upharpoonright\) \upharpoonright \(\downharpoonright\) \downharpoonleft
\(\rightleftharpoons\) \rightleftharpoons \(\leftrightharpoons\) \leftrightharpoons
\(\rightrightarrows\) \rightrightarrows \(\leftleftarrows\) \leftleftarrows
\(\Rrightarrow\) \Rrightarrow \(\Lleftarrow\) \Lleftarrow
\(\rightleftarrows\) \rightleftarrows \(\leftrightarrows\) \rightleftarrows
\(\nrightarrow\) \nrightarrow \(\nleftarrow\) \nleftarrow
\(\nLeftarrow\) \nLeftarrow \(\nRightarrow\) \nRightarrow
\(\nleftrightarrow\) \nleftrightarrow \(\curvearrowleft\) \curvearrowleft
\(\circlearrowleft\) \circlearrowleft \(\curvearrowright\) \curvearrowright
\(\circlearrowright\) \circlearrowright \(\looparrowleft\) \looparrowleft
\(\rightarrowtail\) \rightarrowtail \(\looparrowright\) \looparrowright
\(\leftarrowtail\) \leftarrowtail \(\Lsh\) \Lsh
\(\twoheadleftarrow\) \twoheadleftarrow \(\Rsh\) \Rsh
\(\twoheadrightarrow\) \twoheadrightarrow \(\rightsquigarrow\) \rightsquigarrow
\(\leftrightsquigarrow\) \leftrightsquigarrow

几何和向量

显示 符号 显示 符号
\(\triangle\) \triangle \(\Diamond\) \Diamond
\(\Box\) \Box \(\odot\) \odot
\(\angle ABC\) \angle ABC \(30^\circ\) 30^\circ
\(\perp\) \perp \(\sim\) \sim
\(\cong\) \cong \(\hat{a}\) \hat{a}
\(\vec{a}\) \vec{a} \(\overrightarrow{AB}\) \overrightarrow{AB}
\(\overleftarrow{AB}\) \overleftarrow{AB} \(\overleftrightarrow{AB}\) \overleftrightarrow{AB}
\(\widehat{e f g}\) \widehat{e f g}

音调

显示 符号 显示 符号
\(\bar a\) \bar a \(\acute{a}\) \acute{a}
\(\check{a}\) \check{a} \(\grave{a}\) \grave{a}
\(\breve{a}\) \breve{a} \(\dot{a}\) \dot{a}
\(\ddot{a}\) \ddot{a} \(\dddot{a}\) \dddot{a}
\(\hat a\) \hat{a} \(\tilde{a}\) \tilde

上、下划线和上、下括号

显示 符号
\(\overline{h i j}\) \overline{h i j}
\(\underline{h i j}\) \underline{h i j}
$\underbrace{a+b+\cdots+z}_{10}\ $ \underbrace{a+b+\cdots+z}_{10}
\(\overbrace{a+b+\cdots+z}^{10}\) \overbrace{a+b+\cdots+z}^{10}

特殊字符

符号 显示 符号 显示 符号 显示
\(\eth\) \eth \(\S\) \S \(\P\) \P
\(\%\) \% \(\dagger\) \dagger \(\ddagger\) \ddagger
\(\star\) \star \(\ast\) \ast* \(\circ\) \circ
\(\bullet\) \bullet \(\ldots\) \ldots \(\cdots\) \cdots
\(\vdots\) \vdots \(\ddots\) \ddots \(\smile\) \smile
\(\frown\) \frown \(\wr\) \wr \(\oplus\) \oplus
\(\bigoplus\) \bigoplus \(\otimes\) \otimes \(\bigotimes\) \bigotimes
\(\bigodot\) \bigodot \(\boxtimes\) \boxtimes \(\boxplus\) \boxplus
\(\triangleleft\) \triangleleft \(\triangleright\) \triangleright \(\bot\) \bot
\(\top\) \top \(\vdash\) \vdash \(\Vdash\) \Vdash
\(\vDash\) \vDash \(\models\) \models \(\infty\) \infty
\(\imath\) \imath \(\hbar\) \hbar \(\ell\) \ell
\(\mho\) \mho \(\Finv\) \Finv \(\Re\) \Re
\(\Im\) \Im \(\wp\) \wp \(\diamondsuit\) \diamondsuit
\(\heartsuit\) \heartsuit \(\clubsuit\) \clubsuit \(\spadesuit\) \spadesuit
\(\Game\) \Game \(\flat\) \flat \(\natural\) \natural
\(\sharp\) \sharp \(\because\) \because \(\therefore\) \therefore

阵列

语法: $$\begin{array}…\end{array}$$r右对齐,l左对齐,c居中,|垂直线,\hline横线,\\换行,元素之间以&间隔。

示例:

$$
  \begin{array}{c|lcr}
    n & \text{Left} & \text{Center} & \text{Right} \\
    \hline
    1 & 0.24 & 1 & 125 \\
    2 & -1 & 189 & -8 \\
    3 & -20 & 2000 & 1+10i
  \end{array}
$$

\[\begin{array}{c|lcr} n & \text{Left} & \text{Center} & \text{Right} \\ \hline 1 & 0.24 & 1 & 125 \\ 2 & -1 & 189 & -8 \\ 3 & -20 & 2000 & 1+10i \end{array} \]

矩阵

语法: $$\begin{matrix}…\end{matrix}$$,每行以\\结尾,元素之间以&间隔。

示例:

$$
  \begin{matrix}
    1 & x & x^2 \\
    1 & y & y^2 \\
    1 & z & z^2 \\
  \end{matrix}
$$

\[\begin{matrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \\ \end{matrix} \]

添加括号:

  • pmatrix\(()\)
  • bmatrix\([\ ]\)
  • Bmatrix\(\{\ \}\)
  • vmatrix\(\vert \ \vert\)
  • Vmatrix\(\Vert \ \Vert\)

添加省略号:

\begin{pmatrix}
  1 & a_1^2 & a_1^2 & \cdots & a_1^2 \\
  1 & a_2^2 & a_2^2 & \cdots & a_2^2 \\
  \vdots & \vdots & \vdots & \ddots & \vdots \\
  1 & a_n^2 & a_n^2 & \cdots & a_n^2 \\
\end{pmatrix}

\[\begin{pmatrix} 1 & a_1^2 & a_1^2 & \cdots & a_1^2 \\ 1 & a_2^2 & a_2^2 & \cdots & a_2^2 \\ \vdots & \vdots & \vdots & \ddots & \vdots \\ 1 & a_n^2 & a_n^2 & \cdots & a_n^2 \\ \end{pmatrix} \]

水平增广矩阵: 使用阵列语法,

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

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

垂直增广矩阵:

$$
  \begin{pmatrix}
    a & b\\
    c & d\\
    \hline
    1 & 0\\
    0 & 1
  \end{pmatrix}
$$

\[\begin{pmatrix} a & b\\ c & d\\ \hline 1 & 0\\ 0 & 1 \end{pmatrix} \]

在行内插入矩阵:\(\big( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \big)\)的语法$\big( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \big)$

等式对齐

语法: \begin{align}…\end{align},每行以\\结尾,元素之间以&间隔。

示例:

$$
  \begin{align}
    \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\
     & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ 
     & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\
     & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ 
     & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right)
  \end{align}
$$

\[\begin{align} \sqrt{37} & = \sqrt{\frac{73^2-1}{12^2}} \\ & = \sqrt{\frac{73^2}{12^2}\cdot\frac{73^2-1}{73^2}} \\ & = \sqrt{\frac{73^2}{12^2}}\sqrt{\frac{73^2-1}{73^2}} \\ & = \frac{73}{12}\sqrt{1 - \frac{1}{73^2}} \\ & \approx \frac{73}{12}\left(1 - \frac{1}{2\cdot73^2}\right) \end{align} \]

分段函数

语法: \begin{cases}…\end{cases},每行以\\结尾,元素之间以&间隔。

示例:

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

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

$$  
  \left.
    \begin{array}{l}
    \text{if $n$ is even:}&n/2\\
    \text{if $n$ is odd:}&3n+1
    \end{array}
  \right\}
  =f(n)
$$

\[\left. \begin{array}{l} \text{if $n$ is even:}&n/2\\ \text{if $n$ is odd:}&3n+1 \end{array} \right\} =f(n) \]

编号

语法:\tag

示例:

$$ 
  y=x^2        \tag{1.5a}
$$

\[y=x^2 \tag{1.5a} \]

posted @ 2021-01-13 13:44  yw_sun  阅读(7883)  评论(0编辑  收藏  举报