Latex Math
目錄
直接符號
直接從鍵盤訪問的符號：
\[+ - = ! / ( ) [ ] < > | ' : * \ \]
數學表達式
\pm \mp
\[\pm \mp \]
根
\sqrt{\frac{a}{b}}
\sqrt [ a ] {b} \quad
\[\sqrt{\frac{a}{b}} \sqrt [ a ] {b} \quad \]
積分
\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}
\[\sqrt[n]{1+x+x^2+x^3+\dots+x^n} \]
指數
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}
\[f(n) = n^5 + 4n^2 + 2 |_{n=17} \]
分數
\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
\[^3/_7 \]
連分數
\begin{equation}
x = a_0 + \cfrac{1}{a_1
+ \cfrac{1}{a_2
+ \cfrac{1}{a_3 + \cfrac{1}{a_4} } } }
\end{equation}
\[\begin{equation} x = a_0 + \cfrac{1}{a_1 + \cfrac{1}{a_2 + \cfrac{1}{a_3 + \cfrac{1}{a_4} } } } \end{equation} \]
數的乘法
\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}
\[\begin{equation} \frac{ \begin{array}[b]{r} \left( x_1 x_2 \right)\\ \times \left( x'_1 x'_2 \right) \end{array} }{ \left( y_1y_2y_3y_4 \right) } \end{equation} \]
矩陣和數組
基本矩陣
\begin{matrix}
a & b & c \\
d & e & f \\
g & h & i
\end{matrix}
\[\begin{matrix} a & b & c \\ d & e & f \\ g & h & i \end{matrix} \]
要指定表格中列的對齊方式，請使用帶*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、垂直和對角三組點（稱為橢圓(ellipses)）來填充某些列和行。這些可以分別使用\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}
\[A_{m,n} = \begin{pmatrix} a_{1,1} & a_{1,2} & \cdots & a_{1,n} \\ a_{2,1} & a_{2,2} & \cdots & a_{2,n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m,1} & a_{m,2} & \cdots & a_{m,n} \end{pmatrix} \]
數組環境
\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}
\[M = \begin{bmatrix} \frac{5}{6} & \frac{1}{6} & 0 \\[0.3em] \frac{5}{6} & 0 & \frac{1}{6} \\[0.3em] 0 & \frac{5}{6} & \frac{1}{6} \end{bmatrix} \]
運算符
運算符是一個用單詞表示的函數
如三角函數（sin, cos, tan），對數和/指數（log, exp），極限（lim），以及跡和行列式（tr, det）
\[\arccos \cos \csc \exp \ker \limsup \min \\ \arcsin \cosh \deg \gcd \lg \ln \Pr\\ \arctan \cot \det \hom \lim \log \sec\\ \arg \coth \dim \inf \liminf \max \sin\\ \sinh \sup \tan \tanh \]
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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
控制水平間距
| 命令 | 描述 | 尺寸 | |
|---|---|---|---|
\, |
小空間 | 四邊形的 3/18 | \(\int y \, \mathrm { d } x\) |
\: |
中等空間 | 四邊形的 4/18 | \(\int y \: \mathrm { d } x\) |
\; |
大空間 | 四邊形的 5/18 | \(\int y \; \mathrm { d } x\) |
\! |
負空間 | 四邊形的-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}
\[f(n) = \begin{cases} n/2 & \quad \text{if } n \text{ is even}\\ -(n+1)/2 & \quad \text{if } n \text{ is odd} \end{cases} \]
點
| 代碼 | 輸出 | 評論 |
|---|---|---|
\dots |
\(\dots\) | 通用點（省略號），用於文本（公式之外）。它根據上下文自動管理自身前后的空格，這是一個更高級別的命令。 |
\ldots |
\(\ldots\) | 輸出與上一個類似，但沒有自動空白管理；它在較低級別上工作。 |
\cdots |
\(\cdots\) | 這些點相對於字母的高度居中。還有\cdot下面提到的二元乘法運算符 。 |
\vdots |
\(\vdots\) | 垂直點 |
\ddots |
\(\ddots\) | 對角點 |
\iddots |
\(\iddots\) | 反向對角點（需要mathdots包） |
\hdotsfor{n} |
\(\hdotsfor{n}\) | 要在矩陣中使用，它會創建一行跨越n列的點。 |
向方程添加文本
50 \text{ apples} \times 100 \text{ apples}
= \text{lots of apples}^2
\[50 \text{ apples} \times 100 \text{ apples} = \text{lots of apples}^2 \]
顏色
在Colors中描述的包xcolor允許我們為方程添加顏色。
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
\[\color{yellow} A \color{magenta}= \color{blue}{B} \mathbin{\color{red}-}% shorter than \mathbin{\color{red}{-}} \color{green}{C} \color{cyan}+ D \]
數學符號列表
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 |
格式化數學符號
\mathnormal{…}默認數學字體
\[\mathnormal{ABCDEF abcdef 123456} \]
\mathrm{…}這是默認或普通字體，單位化，計量單位，一字功能
\[\mathrm{ABCDEF abcdef 123456} \]
\mathit{…}斜體字體
\[\mathit{ABCDEF abcdef 123456} \]
\mathbf{…}粗體，矢量圖
\[\mathbf{ABCDEF abcdef 123456} \]
\mathsf{…}無襯線字體
\[\mathsf{ABCDEF abcdef 123456} \]
\mathtt{…}等寬
\[\mathtt{ABCDEF abcdef 123456} \]
\mathbb{…}黑板粗體，用於表示特殊集合（例如實數）
\[\mathbb{ABCDEF abcdef 123456} \]
\mathcal{…}書法（僅限大寫），通常用於輪/方案和類別，用於表示密碼學概念
\[\mathcal{ABCDEF abcdef 123456} \]
\mathscr{…}
\[\mathscr{ABCDEF abcdef 123456} \]
\mathfrak{…}
\[\mathfrak{ABCDEF abcdef 123456} \]
關系符號
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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/或邏輯符號
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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} |
希臘字母
\[\alpha,\Alpha,\beta,\Beta,\gamma,\Gamma,\pi,\Pi,\phi,\varphi,\mu,\Phi \]
| 符號 | Script | 符號 | 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
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | 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
| 符號 | Script | 符號 | Script | 符號 | Script | 符號 | Script |
|---|---|---|---|---|---|---|---|
| \(|\)或\(\mid（間距不同）\) | ` | 或\mid（間距不同）` |
\(|\) | | |
\(/\) | / |
\(\backslash\) |
| \(\{\) | \{ |
\(\}\) | \} |
\(\langle\) | \langle |
\(\rangle\) | \rangle |
| \(\uparrow\) | \uparrow |
\(\Uparrow\) | \Uparrow |
\(\lceil\) | \lceil |
\(\rceil\) | \rceil |
| \(\downarrow\) | \downarrow |
\(\Downarrow\) | \Downarrow |
\(\lfloor\) | \lfloor |
\(\rfloor\) | \rfloor |
| \(\lmoustache\) | \lmoustache |
\(\lmoustache\) | \lmoustache |