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
为\(C_n^2\)。
前置上下标{}_1^2\!X_3^4
为\({}_1^2\!C_3^4\)。
分组
把相同等级的表达式放到一起。
符号: {}
如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} 或\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 或\leq |
\(\ge\) | \ge 或\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 或\wedge |
\(\lor\) | \lor 或\vee |
\(\lnot\) | \lnot 或\neg |
\(\forall\) | \forall |
\(\exists\) | \exists |
\(\top\) | \top |
\(\vdash\) | \vdash |
\(\vDash\) | \vDash |
\(\bot\) | \bot |
括号
括号 | 符号 |
---|---|
\((x)\) | (x) |
\(\{ x \}\) | \{ x \} 或\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 或\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 或* |
\(\circ\) | \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:如\(\big( \begin{smallmatrix} a & b \\ c & d \end{smallmatrix} \big)\)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:
$$
y=x^2 \tag{1.5a}
$$
\[y=x^2 \tag{1.5a}
\]