Latex Math 数学公式 符号
Latex Math
目录
直接符号
直接从键盘访问的符号:
\[+ - = ! / ( ) [ ] < > | ' : * \
\]
数学表达式
\pm \mp
\[\pm
\mp
\]
根
\sqrt{\frac{a}{b}}
\sqrt [ a ] {b} \quad
\[\sqrt{\frac{a}{b}}
\sqrt [ a ] {b} \quad
\]
积分
\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x
\[\int_0^\infty \mathrm{e}^{-x}\,\mathrm{d}x
\]
\int\limits_a^b \iint\limits_a^b
\[\int\limits_a^b \iint\limits_a^b
\]
和
\sum_{i=1}^{10} t_i 或者 \displaystyle\sum_{i=1}^{10} t_i
\[\sum_{i=1}^{10} t_i
\]
\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
\[\sqrt[n]{1+x+x^2+x^3+\dots+x^n}
\]
指数
k_{n+1} = n^2 + k_n^2 - k_{n-1}
\[k_{n+1} = n^2 + k_n^2 - k_{n-1}
\]
f(n) = n^5 + 4n^2 + 2 |_{n=17}
\[f(n) = n^5 + 4n^2 + 2 |_{n=17}
\]
分数
\frac { n! }{ k!(nk)! } = \binom { n }{ k }
\[\frac { n! }{ k!(nk)! } = \binom { n }{ k }
\]
\frac { \frac { 1 } { x } + \frac { 1 } { y }} { y-z }
\[\frac { \frac { 1 } { x } + \frac { 1 } { y }} { y-z }
\]
^3/_7
\[^3/_7
\]
连分数
\begin{equation}
x = a_0 + \cfrac{1}{a_1
+ \cfrac{1}{a_2
+ \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }
\end{equation}
\[\begin{equation}
x = a_0 + \cfrac{1}{a_1
+ \cfrac{1}{a_2
+ \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }
\end{equation}
\]
数的乘法
\begin{equation}
\frac{
\begin{array}[b]{r}
\left( x_1 x_2 \right)\\
\times \left( x'_1 x'_2 \right)
\end{array}
}{
\left( y_1y_2y_3y_4 \right)
}
\end{equation}
\[\begin{equation}
\frac{
\begin{array}[b]{r}
\left( x_1 x_2 \right)\\
\times \left( x'_1 x'_2 \right)
\end{array}
}{
\left( y_1y_2y_3y_4 \right)
}
\end{equation}
\]
矩阵和数组
基本矩阵
\begin{matrix}
a & b & c \\
d & e & f \\
g & h & i
\end{matrix}
\[\begin{matrix}
a & b & c \\
d & e & f \\
g & h & i
\end{matrix}
\]
要指定表格中列的对齐方式,请使用带*
的版本
\begin{matrix}
-1 & 3 \\
2 & -4
\end{matrix}
=
\begin{matrix*}[r]
-1 & 3 \\
2 & -4
\end{matrix*}
\[\begin{matrix}
-1 & 3 \\
2 & -4
\end{matrix}
=
\begin{matrix*}[r]
-1 & 3 \\
2 & -4
\end{matrix*}
\]
通常使用水平、垂直和对角三组点(称为椭圆(ellipses))来填充某些列和行。这些可以分别使用\cdots
,\vdots
和指定\ddots
:
A_{m,n} =
\begin{pmatrix}
a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m,1} & a_{m,2} & \cdots & a_{m,n}
\end{pmatrix}
\[A_{m,n} =
\begin{pmatrix}
a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\
a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\
\vdots & \vdots & \ddots & \vdots \\
a_{m,1} & a_{m,2} & \cdots & a_{m,n}
\end{pmatrix}
\]
数组环境
\begin{array}{c|c}
1 & 2 \\
\hline
3 & 4
\end{array}
\[\begin{array}{c|c}
1 & 2 \\
\hline
3 & 4
\end{array}
\]
M = \begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\[0.3em]
\frac{5}{6} & 0 & \frac{1}{6} \\[0.3em]
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}
\[M = \begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\[0.3em]
\frac{5}{6} & 0 & \frac{1}{6} \\[0.3em]
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}
\]
运算符
运算符是一个用单词表示的函数
如三角函数(sin, cos, tan),对数和/指数(log, exp),极限(lim),以及迹和行列式(tr, det)
\[\arccos \cos \csc \exp \ker \limsup \min \\
\arcsin \cosh \deg \gcd \lg \ln \Pr\\
\arctan \cot \det \hom \lim \log \sec\\
\arg \coth \dim \inf \liminf \max \sin\\
\sinh \sup \tan \tanh
\]
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(\times\) | \times |
\(\div\) | \div |
\(\csc\) | \csc |
\(\sec\) | \sec |
\(\exp\) | \exp |
\(\ker\) | \ker |
\(\limsup\) | \limsup |
\(\sup\) | \sup |
\(\max\) | \max |
\(\min\) | \min |
\(\arcsin\) | \arcsin |
\(\arccos\) | \arccos |
\(\cos\) | \cos |
\(\cosh\) | \cosh |
\(\deg\) | \deg |
\(\gcd\) | \gcd |
\(\lg\) | \lg |
\(\ln\) | \ln |
\(\Pr\) | \Pr |
\(\liminf\) | \liminf |
\(\det\) | \det |
\(\hom\) | \hom |
\(\lim\) | \lim |
\(\log\) | \log |
\(\arg\) | \arg |
\(\coth\) | \coth |
\(\dim\) | \dim |
\(\inf\) | \inf |
\(\sin\) | \sin |
\(\sinh\) | \sinh |
\(\cot\) | \cot |
\(\arctan\) | \arctan |
\(\tan\) | \tan |
\(\tanh\) | \tanh |
\(\mod n\) | \mod |
\(\pmod n\) | \pmod |
\(\equiv\) | \equiv |
\(\bmod\) | \bmod |
\cos (2 \theta )= \cos ^ 2 \theta- \ sin ^ 2 \theta
\[\cos (2 \theta )= \cos ^ 2 \theta- \ sin ^ 2 \theta
\]
\lim\limits _{ x \to \infty } \exp (-x) = 0
\[\lim\limits _{ x \to \infty } \exp (-x) = 0
\]
格式部分
控制水平间距
命令 | 描述 | 尺寸 | |
---|---|---|---|
\, |
小空间 | 四边形的 3/18 | \(\int y \, \mathrm { d } x\) |
\: |
中等空间 | 四边形的 4/18 | \(\int y \: \mathrm { d } x\) |
\; |
大空间 | 四边形的 5/18 | \(\int y \; \mathrm { d } x\) |
\! |
负空间 | 四边形的-3/18 | \(\int y \! \mathrm { d } x\) |
f(n) =
\begin{cases}
n/2 & \quad \text{if } n \text{ is even}\\
-(n+1)/2 & \quad \text{if } n \text{ is odd}
\end{cases}
\[f(n) =
\begin{cases}
n/2 & \quad \text{if } n \text{ is even}\\
-(n+1)/2 & \quad \text{if } n \text{ is odd}
\end{cases}
\]
点
代码 | 输出 | 评论 |
---|---|---|
\dots |
\(\dots\) | 通用点(省略号),用于文本(公式之外)。它根据上下文自动管理自身前后的空格,这是一个更高级别的命令。 |
\ldots |
\(\ldots\) | 输出与上一个类似,但没有自动空白管理;它在较低级别上工作。 |
\cdots |
\(\cdots\) | 这些点相对于字母的高度居中。还有\cdot 下面提到的二元乘法运算符 。 |
\vdots |
\(\vdots\) | 垂直点 |
\ddots |
\(\ddots\) | 对角点 |
\iddots |
\(\iddots\) | 反向对角点(需要mathdots包) |
\hdotsfor{n} |
\(\hdotsfor{n}\) | 要在矩阵中使用,它会创建一行跨越n列的点。 |
向方程添加文本
50 \text{ apples} \times 100 \text{ apples}
= \text{lots of apples}^2
\[50 \text{ apples} \times 100 \text{ apples}
= \text{lots of apples}^2
\]
颜色
在Colors中描述的包xcolor允许我们为方程添加颜色。
black, blue, brown, cyan, darkgray, gray, green, lightgray, lime, magenta, olive, orange, pink, purple, red, teal, violet, white, yellow.
k = {\color{red}x} \mathbin{\color{blue}-} 2
\[k = {\color{red}x} \mathbin{\color{blue}-} 2
\]
\color{red} C^2 \\
\color{yellow} A = \color{blue}{B} \mathbin{\color{red}{-}} \color{green}{C}
\[\color{red} C^2 \\
\color{yellow} A = \color{blue}{B} \mathbin{\color{red}{-}} \color{green}{C}
\]
\color{yellow} A \color{magenta}=
\color{blue}{B}
\mathbin{\color{red}-}% shorter than \mathbin{\color{red}{-}}
\color{green}{C}
\color{cyan}+
D
\[\color{yellow} A \color{magenta}=
\color{blue}{B}
\mathbin{\color{red}-}% shorter than \mathbin{\color{red}{-}}
\color{green}{C}
\color{cyan}+
D
\]
数学符号列表
常用
\(\sum\) | \sum |
\(\prod\) | \prod |
\(\coprod\) | \coprod |
\(\bigoplus\) | \bigoplus |
\(\bigotimes\) | \bigotimes |
\(\bigodot\) | \bigodot |
\(\bigcup\) | \bigcup |
\(\bigcap\) | \bigcap |
\(\biguplus\) | \biguplus |
\(\bigsqcup\) | \bigsqcup |
\(\bigvee\) | \bigvee |
\(\bigwedge\) | \bigwedge |
\(\int\) | \int |
\(\oint\) | \oint |
\(\iint\) | \iint |
\(\iiint\) | \iiint |
\(\iiiint\) | \iiiint |
\(\idotsint\) | \idotsint |
格式化数学符号
\mathnormal{…}
默认数学字体
\[\mathnormal{ABCDEF abcdef 123456}
\]
\mathrm{…}
这是默认或普通字体,单位化,计量单位,一字功能
\[\mathrm{ABCDEF abcdef 123456}
\]
\mathit{…}
斜体字体
\[\mathit{ABCDEF abcdef 123456}
\]
\mathbf{…}
粗体,矢量图
\[\mathbf{ABCDEF abcdef 123456}
\]
\mathsf{…}
无衬线字体
\[\mathsf{ABCDEF abcdef 123456}
\]
\mathtt{…}
等宽
\[\mathtt{ABCDEF abcdef 123456}
\]
\mathbb{…}
黑板粗体,用于表示特殊集合(例如实数)
\[\mathbb{ABCDEF abcdef 123456}
\]
\mathcal{…}
书法(仅限大写),通常用于轮/方案和类别,用于表示密码学概念
\[\mathcal{ABCDEF abcdef 123456}
\]
\mathscr{…}
\[\mathscr{ABCDEF abcdef 123456}
\]
\mathfrak{…}
\[\mathfrak{ABCDEF abcdef 123456}
\]
关系符号
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(.\) | . |
\(<\) | < |
\(>\) | > |
\(=\) | = |
\(\parallel\) | \parallel |
\(\nparallel\) | \nparallel |
\(\leq\) | \leq |
\(\geq\) | \geq |
\(\doteq\) | \doteq |
\(\asymp\) | \asymp |
\(\bowtie\) | \bowtie |
\(\ll\) | \ll |
\(\gg\) | \gg |
\(\equiv\) | \equiv |
\(\vdash\) | \vdash |
\(\dashv\) | \dashv |
\(\subset\) | \subset |
\(\supset\) | \supset |
\(\approx\) | \approx |
\(\in\) | \in |
\(\ni\) | \ni |
\(\subseteq\) | \subseteq |
\(\supseteq\) | \supseteq |
\(\cong\) | \cong |
\(\smile\) | \smile |
\(\frown\) | \frown |
\(\nsubseteq\) | \nsubseteq |
\(\nsupseteq\) | \nsupseteq |
\(\simeq\) | \simeq |
\(\models\) | \models |
\(\notin\) | \notin |
\(\sqsubset\) | \sqsubset |
\(\sqsupset\) | \sqsupset |
\(\sim\) | \sim |
\(\perp\) | \perp |
\(\mid\) | \mid |
\(\sqsubseteq\) | \sqsubseteq |
\(\sqsupseteq\) | \sqsupseteq |
\(\propto\) | \propto |
\(\prec\) | \prec |
\(\succ\) | \succ |
\(\preceq\) | \preceq |
\(\succeq\) | \succeq |
\(\neq\) | \neq |
\(\sphericalangle\) | \sphericalangle |
\(\measuredangle\) | \measuredangle |
\(\therefore\) | \therefore |
\(\because\) | \because |
\(\thicksim\) | \thicksim |
\(\backsim\) | \backsim |
二元操作
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(\pm\) | \pm |
\(\cap\) | \cap |
\(\diamond\) | \diamond |
\(\oplus\) | \oplus |
\(\mp\) | \mp |
\(\cup\) | \cup |
\(\bigtriangleup\) | \bigtriangleup |
\(\ominus\) | \ominus |
\(\times\) | \times |
\(\uplus\) | \uplus |
\(\bigtriangledown\) | \bigtriangledown |
\(\otimes\) | \otimes |
\(\div\) | \div |
\(\sqcap\) | \sqcap |
\(\triangleleft\) | \triangleleft |
\(\oslash\) | \oslash |
\(\ast\) | \ast |
\(\sqcup\) | \sqcup |
\(\triangleright\) | \triangleright |
\(\odot\) | \odot |
\(\star\) | \star |
\(\vee\) | \vee |
\(\bigcirc\) | \bigcirc |
\(\circ\) | \circ |
\(\dagger\) | \dagger |
\(\wedge\) | \wedge |
\(\bullet\) | \bullet |
\(\setminus\) | \setminus |
\(\ddagger\) | \ddagger |
\(\cdot\) | \cdot |
\(\wr\) | \wr |
\(\amalg\) | \amalg |
集合和/或逻辑符号
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(\exists\) | \exists |
\(\rightarrow\) | \rightarrow 或\to |
\(\nexists\) | \nexists |
\(\leftarrow\) | \leftarrow 或\gets |
\(\forall\) | \forall |
\(\mapsto\) | \mapsto |
\(\neg\) | \neg |
\(\implies\) | \implies |
\(\cap\) | \cap |
\(\cup\) | \cup |
\(\subset\) | \subset |
\(\impliedby\) | \impliedby |
\(\supset\) | \supset |
\(\Rightarrow\) | \Rightarrow |
\(\in\) | \in |
\(\leftrightarrow\) | \leftrightarrow |
\(\notin\) | \notin |
\(\iff\) | \iff |
\(\ni\) | \ni |
\(\Leftrightarrow\) | \Leftrightarrow |
\(\land\) | \land |
\(\top\) | \top |
\(\lor\) | \lor |
\(\bot\) | \bot |
\(\angle\) | \angle |
\(\emptyset\) | \emptyset |
\(\varnothing\) | \varnothing |
\(\rightleftharpoons\) | \rightleftharpoons |
重音符
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(\hat{a}\) | \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} |
希腊字母
\[\alpha,\Alpha,\beta,\Beta,\gamma,\Gamma,\pi,\Pi,\phi,\varphi,\mu,\Phi
\]
符号 | Script | 符号 | Script |
---|---|---|---|
\(A\)and\(\alpha\) | A \alpha |
\(N\)and\(\nu\) | N \nu |
\(B\)and\(\beta\) | B \beta |
\(\Xi\)and\(\xi\) | \Xi \xi |
\(\Gamma\)and\(\gamma\) | \Gamma \gamma |
\(O\)and\(o\) | O o |
\(\Delta\)and\(\delta\) | \Delta \delta |
\(\Pi\),\(\pi\)and\(\varpi\) | \Pi ,\pi \varpi |
\(E\),\(\epsilon\)and\(\varepsilon\) | E \epsilon \varepsilon |
\(P\),\(\rho\)and\(\varrho\) | P ,\rho \varrho |
\(Z\)and\(\zeta\) | Z \zeta |
\(\Sigma\),\(\sigma\)and\(\varsigma\) | \Sigma \sigma \varsigma |
\(H\)and\(\eta\) | H \eta |
\(T\)and\(\tau\) | T \tau |
\(\Theta\),\(\theta\)and\(\vartheta\) | \Theta \theta \vartheta |
\(\Phi\),\(\phi\)and\(\varphi\) | \Phi \phi \varphi |
\(\Upsilon\)and\(\upsilon\) | \Upsilon \upsilon |
\(I\)and\(\iota\) | I \iota |
\(K\),\(\kappa\)and\(\varkappa\) | K ,\kappa \varkappa |
\(\Omega\)and\(\omega\) | \Omega \omega |
\(X\)and\(\chi\) | X \chi |
\(\Lambda\)and\(\lambda\) | \Lambda \lambda |
\(\Psi\)and\(\psi\) | \Psi \psi |
\(M\)and\(\mu\) | M \mu |
奇奇怪怪的字符
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(\partial\) | \partial |
\(\imath\) | \imath |
\(\Re\) | \Re |
\(\nabla\) | \nabla |
\(\aleph\) | \aleph |
\(\eth\) | \eth |
\(\jmath\) | \jmath |
\(\Im\) | \Im |
\(\Box\) | \Box |
\(\beth\) | \beth |
\(\hbar\) | \hbar |
\(\ell\) | \ell |
\(\wp\) | \wp |
\(\infty\) | \infty |
\(\gimel\) | \gimel |
\(\heartsuit\) | \heartsuit |
\(\sharp\) | \sharp |
$\natural $ | \natural |
\(\clubsuit\) | \clubsuit |
\(\spadesuit\) | \spadesuit |
分隔符
符号 | Script | 符号 | Script | 符号 | Script | 符号 | Script |
---|---|---|---|---|---|---|---|
\(|\)或\(\mid(间距不同)\) | ` | 或 \mid(间距不同)` |
\(|\) | | |
\(/\) | / |
\(\backslash\) |
\(\{\) | \{ |
\(\}\) | \} |
\(\langle\) | \langle |
\(\rangle\) | \rangle |
\(\uparrow\) | \uparrow |
\(\Uparrow\) | \Uparrow |
\(\lceil\) | \lceil |
\(\rceil\) | \rceil |
\(\downarrow\) | \downarrow |
\(\Downarrow\) | \Downarrow |
\(\lfloor\) | \lfloor |
\(\rfloor\) | \rfloor |
\(\lmoustache\) | \lmoustache |
\(\lmoustache\) | \lmoustache |