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Latex Math 数学公式 符号

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Latex Math 目录 Latex Math 直接符号 数学表达式 根 积分 和 指数 分数 连分数 数的乘法 矩阵和数组 运算符 格式部分 控制水平间距 点 向方程添加文本 颜色 数学符号列表 格式化数学符号
Latex Math

目录
  • Latex Math
    • 直接符号
    • 数学表达式
        • 积分
        • 指数
        • 分数
        • 连分数
        • 数的乘法
        • 矩阵和数组
    • 运算符
    • 格式部分
        • 控制水平间距
        • 向方程添加文本
        • 颜色
    • 数学符号列表
      • 格式化数学符号
      • 关系符号
      • 二元操作
      • 集合和/或逻辑符号
      • 重音符
    • 希腊字母
      • 奇奇怪怪的字符
    • 分隔符

直接符号

直接从键盘访问的符号:

\[+ - = ! / ( ) [ ] < > | ' : * \ \]

数学表达式
\pm \mp

\[\pm \mp \]

\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

\[\int\limits_a^b \iint\limits_a^b \]

\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\to \(\nexists\) \nexists \(\leftarrow\) \leftarrow\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)$ ` \mid(间距不同)` \(|\) | \(/\) / \(\{\) \{ \(\}\) \} \(\langle\) \langle \(\rangle\) \rangle \(\uparrow\) \uparrow \(\Uparrow\) \Uparrow \(\lceil\) \lceil \(\rceil\) \rceil \(\downarrow\) \downarrow \(\Downarrow\) \Downarrow \(\lfloor\) \lfloor \(\rfloor\) \rfloor \(\lmoustache\) \lmoustache \(\lmoustache\) \lmoustache 【本文转自:韩国服务器 https://www.68idc.cn 复制请保留原URL】
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