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    • latex常用符号

    1. latex常用符号

    1.1. 返回主页

    主页地址 https://kz16.top/

    显示latex格式的公式需要加美元号$，例如$\beta$显示的结果为β\beta，如果单独一行的公式可用双美元符号，例如$$\underset{x}{\min\; }x^2=0$$会单独成行
    min⁡  xx2=0\underset{x}{\min\;} x^2=0

    WPS公式编辑器快捷键
    下角标L_{L} Ctrl + L 上角标H^{H} Ctrl + H
    上下角标JJ_{J}^{J} Ctrl + J 分数线FF\dfrac{F}{F} Ctrl + F
    α,β\alpha,\beta希腊G Ctrl + G 根号R\sqrt{R} Ctrl + R
    积分I Ctrl + I

    Ctrl + 括号 可自动补全括号
    Ctrl + Shift + 空格 可在公式中空格
    Alt + S+M 调整样式为英文
    Alt + I+Q 可以直接调出公式面板

    记忆:

    • 下角标L_L 下楼XL
    • 上角标H^H 上海SH

    1.2. 常用公式
    x=−b∓b2−4ac2ax=\frac{-b\mp\sqrt{b^2-4ac}}{2a} x=\frac{-b\mp\sqrt{b^2-4ac}}{2a}
    x=−b±b2−4ac2ax=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a} x=\dfrac{-b\pm\sqrt{b^2-4ac}}{2a}
    n!=1×2×3⋯×nn! = 1\times2\times3\cdots\times n n! = 1\times2\times3\cdots\times n
    ∮f(s)ds\oint f(s)\mathrm{d}s \oint f(s)\mathrm{d}r
    ∮f(s)ds\displaystyle\oint f(s)\mathrm{d}s \displaystyle\oint f(s)\mathrm{d}s
    ∫−1+∞f(x)dx\displaystyle\int_{-1}^{+\infty} f(x)\mathrm{d}x \displaystyle\int_{-1}^{+\infty} f(x)\mathrm{d}x
    ∬f(x)dx\displaystyle\iint f({\boldsymbol x})\mathrm{d}{\boldsymbol x} \displaystyle\iint f({\boldsymbol x})\mathrm{d}{\boldsymbol x}
    ∥∑i=1p+1∥\left\|\sum_{i=1}^{p+1} \right\| \left\|\sum_{i=1}^{p+1}\right\|
    ∥∑i=1p+1∥\left\|\displaystyle\sum_{i=1}^{p+1} \right\| \left\|\displaystyle\sum_{i=1}^{p+1} \right\|
    ∥∑i=1p+1∥\Big\Vert\displaystyle\sum_{i=1}^{p+1}\bigg\Vert \Big\Vert\displaystyle\sum_{i=1}^{p+1}\bigg\Vert
    ∇⋅∇u=Δu\nabla\cdot\nabla u = \Delta u \nabla\cdot\nabla u = \Delta u
    (a+b+ca+b)\tbinom{a+b+c}{a+b} \tbinom{a+b+c}{a+b}
    (a+b+ca+b)\dbinom{a+b+c}{a+b} \dbinom{a+b+c}{a+b}
    [a+b+ca+b]{a+b+c\brack a+b} {a+b+c\brack a+b}
    {a+b+ca+b}{a+b+c\brace a+b} {a+b+c\brace a+b}
    (a+b+ca+b){a+b+c \choose a+b} {a+b+c \choose a+b}
    (a+ba+b+c)\left(_{a+b}^{a+b+c}\right) \left(_{a+b}^{a+b+c}\right)
    a+ba+b+c{a+b \atop a+b+c} {a+b \atop a+b+c}
    Ca+b+ca+bC_{a+b+c}^{a+b} C_{a+b+c}^{a+b}
    min⁡x∈Rf(x)\min\limits^{x\in\mathcal{R}}f(x) \min\limits^{x\in\mathcal{R}}f(x)
    max⁡x∈Rf(x)\max\limits_{x\in\mathcal{R}}f(x) \max\limits_{x\in\mathcal{R}}f(x)

    dudt=∂u∂x∂x∂t+∂u∂y∂y∂t\dfrac{\mathrm{d}u}{\mathrm{d}t}=\dfrac{\partial u}{\partial x}\dfrac{\partial x}{\partial t} + \dfrac{\partial u}{\partial y}\dfrac{\partial y}{\partial t}

    \dfrac{\mathrm{d}u}{\mathrm{d}t}
=
\dfrac{\partial u}{\partial x}\dfrac{\partial x}{\partial t}
+
\dfrac{\partial u}{\partial y}\dfrac{\partial y}{\partial t}

    1.3. 希腊字母
    α\alpha \alpha θ\theta \theta oo o τ\tau \tau
    β\beta \beta ϑ\vartheta \vartheta π\pi \pi υ\upsilon \upsilon
    γ\gamma \gamma ι\iota \iota ϖ\varpi \varpi ϕ\phi \phi
    δ\delta \delta κ\kappa \kappa ρ\rho \rho φ\varphi \varphi
    ϵ\epsilon \epsilon λ\lambda \lambda ϱ\varrho \varrho χ\chi \chi
    ε\varepsilon \varepsilon μ\mu \mu σ\sigma \sigma ψ\psi \psi
    ζ\zeta \zeta ν\nu \nu ς\varsigma \varsigma ω\omega \omega
    η\eta \eta ζ\zeta \zeta
    Γ\Gamma \Gamma Λ\Lambda \Lambda Σ\Sigma \Sigma Ψ\Psi \Psi
    Δ\Delta \Delta Ξ\Xi \Xi Υ\Upsilon \Upsilon Ω\Omega \Omega
    Θ\Theta \Theta Π\Pi \Pi Φ\Phi \Phi
    ℵ\aleph \aleph ℶ\beth \beth ℸ\daleth \daleth ℷ\gimel \gimel

    1.4. 数学相关
    abcxyz\dfrac{abc}{xyz} \dfrac{abc}{xyz} abcxyz\frac{abc}{xyz} \frac{abc}{xyz} abc‾\overline{abc} \overline{abc}
    abc\sqrt{abc} \sqrt{abc} abcn\sqrt[n]{abc} \sqrt[n]{abc} abc‾\underline{abc} \underline{abc}
    abc^\widehat{abc} \widehat{abc} abc~\widetilde{abc} \widetilde{abc} abc→\overrightarrow{abc} \overrightarrow{abc}
    abc←\overleftarrow{abc} \overleftarrow{abc} abc⏞\overbrace{abc} \overbrace{abc} abc⏟\underbrace{abc} \underbrace{abc}
    ab⌢\overset{\frown} {ab} \overset{\frown}{ab} AB⏠\overgroup{AB} \overparen{ab}

    注：头顶的弧盖\overparen{ab}用于LaTeX\LaTeX, \overgroup{AB}AB⏠\overgroup{AB}用于KaTeX\KaTeX

    1.5. 分割符号
    ∣\vert \vert ⟨\langle \langle ⌊\lfloor \lfoolr ⌈\lceil \lceil
    ∥\Vert \Vert ⟩\rangle \rangle ⌋\rfloor \rfloor ⌉\rceil \rceil
    ⇑\Uparrow \Uparrow ↑\uparrow \uparrow ⇓\Downarrow \Downarrow ↓\downarrow \downarrow
    ⌞\llcorner \llcorner ⌟\lrcorner \lrcorner ⌜\ulcorner \ulcorner ⌝\urcorner \urcorner
    // / \\backslash \backslash

    1.6. 可变公式
    ∑\sum \sum ∏\prod \prod ∐\coprod \coprod
    ∫\int \int ∮\oint \ont ∬\iint \iint
    ⨄\biguplus \biguplus ⋂\bigcap \bigcap ⋃\bigcup \bigcup
    ⨁\bigoplus \bigoplus ⨂\bigotimes \bigotimes ⨀\bigodot \bigodot
    ⋁\bigvee \bigvee ⋀\bigwedge \bigwedge ⨆\bigsqcup \bigsqcup

    1.7. 数学函数

    只需要在常用数学函数前加上斜杠\即可
    $\sin, \cos, \tan, \exp, \min, \max, \log, \ln, \lim, \cdots$
    sin⁡,cos⁡,tan⁡,exp⁡,min⁡,max⁡,log⁡,ln⁡,lim⁡,⋯\sin, \cos, \tan, \exp, \min, \max, \log, \ln, \lim, \cdots

    1.8. 运算符号
    ++ + −- - ×\times \times ÷\div \div
    ∗\ast \ast ⋆\star \star ⋅\cdot \cdot ∘\circ \circ
    ±\pm \pm ∓\mp \mp ⊕\oplus \oplus ⊗\otimes \otimes
    ⋇\divideontimes \divideontimes ⋅\centerdot \centerdot ⊙\odot \odot ⊚\circledcirc \circledcirc
    ∩\cap \cap ∪\cup \cup ∨\vee \vee ∧\wedge \wedge
    ⊥\bot \bot ⊥\perp \perp ∖\setminus \setminus \\backslash \backslash
    □\Box \Box □\square \square ≀\wr \wr ⊞\boxplus \boxplus
    △\triangle \triangle ▽\bigtriangledown \bigtriangledown Δ\Delta \Delta ∇\nabla \nabla
    ≡\equiv \equiv ≠\neq \neq ∼\sim \sim ≈\approx \approx
    ≜\triangleq \triangleq ∝\varpropto \varpropto ≪\ll \ll ⋘\lll \lll
    ≤\leq \leq ≥\geq \geq ⩽\leqslant \leqslant ⩾\geqslant \geqslant
    ∈\in \in ∉\notin \notin ≺\prec \prec ≻\succ \succ
    ⊂\subset \subset ⊆\subseteq \subseteq ⊃\supset \supset ⊇\supseteq \supseteq
    ⫆\supseteqq \supseteqq ⫅\subseteqq \subseteqq ⊈\nsubseteq \nsubseteq ⊈\nsubseteqq \nsubseteqq
    ⊊\subsetneq \subsetneq ⫋\subsetneqq \subsetneqq ⊋\supsetneq \supsetneq ⫌\supsetneqq \supsetneqq
    ∁\complement \complement ≅\cong \cong ≌ \text{≌} ∽ \text{∽}

    相似全等符号≅∼≌∽\text{≅∼≌∽}可以直接输入，建议用\text{≅∼≌∽}

    也可以组合 ∼=\begin{matrix} \sim\\[-0.8em]= \end{matrix} ，\begin{matrix} \sim\\[-0.8em]= \end{matrix}

    1.9. 其它符号
    ∵\because \because ∴\therefore \therefore //// // ⊥\perp \perp
    △\triangle \triangle □\square \square ▱\text{▱} \text{▱} =//{}_{=}^{//} {}_{=}^{//}
    ∞\infty \infty ∠\angle \angle ∡\measuredangle \measuredangle ∢\sphericalangle \sphericalangle
    ∀\forall \foall ∃\exist \exist ∅\varnothing \varnothing ∅\emptyset \emptyset
    ∂\partial \partial ′\prime \prime ℏ\hbar \hbar √\surd \surd
    ⋯\cdots \cdots ⋮\vdots \vdots …\ldots \ldots ⋱\ddots \ddots
    ℑ\Im \Im ℜ\Re \Re ◊\lozenge \lozenge ℧\mho \mho
    ♠\spadesuit \spadesuit ♡\heartsuit \heartsuit ♣\clubsuit \clubsuit ♢\diamondsuit \diamondsuit
    ©\copyright \copyright Ⓢ\circledS \circledS ®\circledR \circledR £\pounds \pounds
    $ \$ %\% \% #\# \# ~ \~{}
    ı\imath \imath ȷ\jmath \jmath ℓ\ell \ell

    注1：平行四边形符号▱并不是内置的latex符号而是特殊字符
    注2：////与=//{}_{=}^{//}是组合生成，并非内置

    1.10. 箭头合集
    →\rightarrow \rightarrow ⟶\longrightarrow \longrightarrow ⇒\Rightarrow \Rightarrow
    ⟹\Longrightarrow \Longrightarrow ←\leftarrow \leftarrow ⟵\longleftarrow \longleftarrow
    ⇐\Leftarrow \Leftarrow ⟸\Longleftarrow \Longleftarrow ↗\nearrow \nearrow
    ↘\searrow \searrow ↙\swarrow \swarrow ↖\nwarrow \nwarrow
    ↦\mapsto \mapsto ⟼\longmapsto \longmapsto ⇝\rightsquigarrow \rightsquigarrow
    ⇉\rightrightarrows \rightrightarrows ↔\leftrightarrow \leftrightarrow ⟷\longleftrightarrow \longleftrightarrow
    ⇔\Leftrightarrow \Leftrightarrow ⟺\Longleftrightarrow \Longleftrightarrow ⇌\rightleftharpoons \rightleftharpoons
    ⇆\leftrightarrows \leftrightarrows ⇋\leftrightharpoons \leftrightharpoons ⇄\rightleftarrows \rightleftarrows
    ↺\circlearrowleft \circlearrowleft ↻\circlearrowright \circlearrowright ⇍\nLeftarrow \nLeftarrow
    ⇏\nRightarrow \nRightarrow ⇎\nLeftrightarrow \nLeftrightarrow ↭\leftrightsquigarrow \leftrightsquigarrow
    ⇢\dashrightarrow \dashrightarrow ⇠\dashleftarrow \dashleftarrow

    1.11. 帽子标记
    aˉ\bar{a} \bar{a} aˊ\acute{a} \acute{a} aˇ\check{a} \check{a} aˋ\grave{a} \grave{a}
    a˙\dot{a} \dot{a} a^\hat{a} \hat{a} a˘\breve{a} \breve{a} a⃗\vec{a} \vec{a}
    a¨\ddot{a} \ddot{a} a~\tilde{a} \tilde{a}

    1.12. 数学样式

    \mathcal{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathcal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathbb{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbb{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathfrak{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathfrak{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathsf{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathsf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathscr{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathscr{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathrm{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathrm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathit{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathit{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathnormal{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathnormal{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \mathbf{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\mathbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \textbf{A} 文本样式粗体
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\textbf{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \text{A} 文本样式
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\text{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \bm{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\bm{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    \boldsymbol{A}
    ABCDEFGHIJKLMNOPQRSTUVWXYZ\boldsymbol{ABCDEFGHIJKLMNOPQRSTUVWXYZ}

    1.13. 大小颜色
    123456789{\color{red}123} {\color{blue}456} {\color{green}789} {\color{red}123} {\color{blue}456} {\color{green}789}
    abc\tiny{abc} \tiny{abc}
    abc\scriptsize{abc} \scriptsize{abc}
    abc\footnotesize{abc} \footnotesize{abc}
    abc\small{abc} \small{abc}
    abc\normalsize{abc} \normalsize{abc}
    abc\large{abc} \large{abc}
    abc\Large{abc} \Large{abc}
    abc\LARGE{abc} \LARGE{abc}
    abc\huge{abc} \huge{abc}
    abc\Huge{abc} \Huge{abc}
    [(([(\left[ \Bigg( \bigg( \Big[ \big( \right. \left[ \Bigg( \bigg( \Big[ \big( \right.
    [{}}]\left[ \bigg\{ \Big\}\big\} \right] \left[ \bigg\{ \Big\}\big\} \right]

    注：\left与\right成对出现，缺省可用.补充，它会自动设置大小

    1.14. 多行公式

    多行公式常用的两环境有cases与aligned

    {x+y=1x−y=1,∫−∞+∞f(x)dx∑k=0nk\begin{cases} x+y=1\\ x-y=1 \end{cases}, \qquad % %后面是接注释，\qquaa表示空格 \begin{aligned} &\int_{-\infty}^{+\infty}f(x)\mathrm{d}x\\[.8em] &\sum_{k=0}^n k \end{aligned}

    \begin{cases}
x+y=1\\
x-y=1
\end{cases},
\qquad % %后面是接注释，\qquaa表示空格
\begin{aligned}
&\int_{-\infty}^{+\infty}f(x)\mathrm{d}x\\[.5em]
&\sum_{k=0}^n k
\end{aligned}
% &字符号表示对齐，\\另起一行, \\[.5em]里面的.5表示行高

    矩阵格式

    (123456789),∣abcd∣,abcdef\left(\begin{matrix} 1&2&3\\ 4&5&6\\ 7&8&9 \end{matrix}\right) ,\qquad \left| \begin{matrix} a&b\\ c&d \end{matrix}\right| ,\qquad \begin{matrix} a&b\\ c&d \\ e&f \end{matrix}

    \left(\begin{matrix}
1&2&3\\
4&5&6\\
7&8&9
\end{matrix}\right)
,\qquad
\left|
\begin{matrix}
a&b\\
c&d
\end{matrix}\right|
,\qquad
\begin{matrix}
a&b\\
c&d \\
e&f
\end{matrix}

    1.15. 间距微调

    间距紧凑：\!
    x+yx+y x+y
    x ⁣+yx\!+y x\!+y
    x ⁣ ⁣+yx\!\!+y x\!\!+y

    间距拉开：\, \; \quad \qquad
    x+yx+y x+y
    x+ yx+\,y x+\,y
    x+  yx+\;y x+\;y
    x+yx+\quad y x+\quad y
    x+yx+\qquad y x+\qquad y

    1.16. 返回主页

    主页地址 https://kz16.top/

    欢迎非商业转载，转载请指明来源，
    本文来源 https://kz16.top/latex/symbol
    作者：Zhou Bingzhen

    本文参考https://katex.org/docs/supported.html