231 lines
4.7 KiB
Markdown
231 lines
4.7 KiB
Markdown
# LaTex 数学公式
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- [LaTex 数学公式](#latex-数学公式)
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- [1. 行内公式与行间公式](#1-行内公式与行间公式)
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- [2. 角标](#2-角标)
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- [3. 运算符](#3-运算符)
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- [4. 希腊字母](#4-希腊字母)
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- [5. 带标字母](#5-带标字母)
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- [6. 常用数集](#6-常用数集)
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- [7. 组合](#7-组合)
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- [7.1. 基本组合](#71-基本组合)
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- [7.2. 矩阵](#72-矩阵)
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- [8. 排版](#8-排版)
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## 1. 行内公式与行间公式
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行内公式使用“\$”进行包含，行间公式使用“$$” 进行包含：
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- 行内公式：$a+b$
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- 行间公式：
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$$a+b$$
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## 2. 角标
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- 下标：$a_0$
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- 上标：$a^n$
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## 3. 运算符
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| Operator | LaTex |
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|----------|-------|
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| + - | + - |
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| × · | \times \cdot |
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| ÷ / | \div \frac{a}{b} |
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| ± ∓ | \pm \mp |
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| () [] {} | () [] \{\} |
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| ⌊ ⌋ | \lfloor \rfloor |
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| ⌈ ⌉ | \lceil \rceil |
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| ∑ ∏ ∐ | \sum \prod \coprod |
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| ∫ ∮ | \int \oint |
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| ⊕, ⊗ ⊙ ⊎ | \oplus \otimes \odot \uplus |
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| ⨁, ⨂ ⨀ ⨄ | \bigoplus \bigotimes \bigodot \biguplus |
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| > < | > < |
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| ≥ ≤ | \geq \leq |
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| ≧ ≦ | \gegg \leqq |
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| ≫ ≪ | \gg \ll |
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| = | = |
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| $\neq$ | \neq |
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| ≡ | \equiv |
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| ≈ | \approx |
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| ∼ | \sim |
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| ∝ | \propto |
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| $\widehat{=}$ | \widehat{=} |
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| : | \colon |
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| ∣ | \mid \| \vert |
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| ⊆ | \subset |
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| ⊂ ⊊ | \subset \subsetneq |
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| ⊇ | \supseteq |
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| ⊃ ⊋ | \supset \supsetneq |
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| $\in \ni$ | \in \ni |
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| $\notin \not\ni$ | \notin \not\ni |
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| ∪ | \cup |
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| ∩ | \cap |
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| \ | \backslash |
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| △ | \triangle |
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| ∪ | \dot\cup
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| ⊔ | \sqcup |
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| C | ^{\mathrm{C}} |
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| $\mathcal{P}$ | \mathcal{P} |
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| $\sqcup {P}$ | \sqcup{P} |
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| $\vee{P}$ | \vee{P} |
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| $\wedge {P}$ | \wedge{P} |
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| $\land p$ | \land p |
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| $\wedge p$ | \wedge p |
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| $\bigwedge p$ | \bigwedge p |
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| $\to p$ | \to p |
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| $\lor p$ | \lor p |
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| $\vee p$ | \vee p |
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| $\bigvee p$ | \bigvee p |
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| $\lnot p$ | \lnot p |
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| $\neg p$ | \neg p |
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| $\setminus p$ | \setminus p |
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| $\smallsetminus p$ | \smallsetminus p |
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## 4. 希腊字母
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| Greek | LaTex |
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|-------|-------|
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| αA | \alpha A |
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| βB | \beta B |
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| γΓ | \gamma \Gamma |
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| δΔ | \delta \ Delta |
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| ϵεE | \epsilon \varepsilon E |
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| ζZ | \zeta Z |
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| ηH | \eta H |
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| θϑΘ | \theta \vartheta \Theta |
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| ιI | \iota I |
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| κK | \kappa K |
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| λΛ | \lambda \Lambda |
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| μM | \mu M |
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| ξΞ | \xi \Xi |
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| oO | o O |
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| πΠ | \pi \Pi |
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| ρϱP | \rho \varrho P |
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| σΣ | \sigma \Sigma |
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| τT | \tau T |
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| υΥ | \upsilon \Upsilon |
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| ϕφΦ | \phi \varphi \Phi |
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| χX | \chi X |
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| ψΨ | \psi \Psi |
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| ωΩ | \omega \Omega |
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| $\int_{a}^{b} x^2 dx$ | \int_{a}^{b} x^2 dx |
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| $\iint_V \mu(u,v) \,du\,dv$ | \iint_V \mu(u,v) \,du\,dv |
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| $\iiint_V \mu(u,v,w) \,du\,dv\,dw$ | \iiint_V \mu(u,v,w) \,du\,dv\,dw |
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| $\sum_{n=-\infty}^{+\infty}$ | \sum_{n=-\infty}^{+\infty} |
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| $\prod_{i=a}^{b}$ | \prod_{i=a}^{b} |
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| $\lim_{x\to\infty} f(x)$ | \lim_{x\to\infty} f(x) |
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## 5. 带标字母
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| Letter | LaTex |
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|--------|-------|
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| $\bar{x}$ | \bar{x} |
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| $\acute{x}$ | \acute{x} |
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| $\check{x}$ | \check{x} |
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| $\grave{x}$ | \grave{x} |
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| $\breve{x}$ | \breve{x} |
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| $\ddot{x}$ | \ddot{x} |
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| $\dot{x}$ | \dot{x} |
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| $\hat{x}$ | \hat{x} |
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| $\tilde{x}$ | \tilde{x} |
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## 6. 常用数集
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| Operator | LaTex |
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|----------|-------|
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| $\mathbb{N}$ | \mathbb{N} |
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| $\mathbb{Z}$ | \mathbb{Z} |
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| $\mathbb{Q}$ | \mathbb{Q} |
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| $\mathbb{R}$ | \mathbb{R} |
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| $\mathbb{A}$ | \mathbb{A} |
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| $\mathbb{C}$ | \mathbb{C} |
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## 7. 组合
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### 7.1. 基本组合
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等式：
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$$\begin{equation}
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f=a+b \\
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\end{equation}$$
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带序号的公式：
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$$\begin{gather}
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a+b=b+a\\
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ab=ba
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\end{gather}$$
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无序号的公式：
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$$\begin{gather*}
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a+b=b+a\\
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ab=ba
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\end{gather*}$$
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利用“\notag”阻止编号：
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$$\begin{gather}
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a+b=b+a \notag\\
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ab=ba
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\end{gather}$$
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将公式对齐：
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$$\begin{align*}
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2a+b=a+2b \\
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a=b
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\end{align*}$$
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分段函数排版：
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$$\begin{equation*}
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D(x)=\begin{cases}
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1,&\text{如果} x \in \mathbb{Q};\\
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0,&\text{如果} x \in \mathbb{R} \setminus \mathbb{Q}.
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\end{cases}
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\end{equation*}$$
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一个公式多行排版：
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$$\begin{split}
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F_s(s)=\int_{0}^{\infty}[\sum_{n=0}^{\infty}f(nT)\delta(t-nT)]e^{-st}dt \\
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=\sum_{n=0}^{\infty}f(nT)e^{-snT} \\
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\end{split}$$
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### 7.2. 矩阵
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$$\begin{matrix}
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0 & 1 \\ 1 & 0 \\
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\end{matrix}$$
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$$\begin{pmatrix}
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0 & 1 \\ 1 & 0 \\
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\end{pmatrix}$$
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$$\begin{bmatrix}
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0 & 1 \\ 1 & 0 \\
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\end{bmatrix}$$
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$$\begin{Bmatrix}
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0 & 1 \\ 1 & 0 \\
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\end{Bmatrix}$$
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$$\begin{vmatrix}
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0 & 1 \\ 1 & 0 \\
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\end{vmatrix}$$
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$$\begin{Vmatrix}
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0 & 1 \\ 1 & 0 \\
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\end{Vmatrix}$$
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## 8. 排版
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| LaTex | Description |
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|-------|-------------|
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| \\ | 换行 |
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| & | 间隔，相当于 Tab |
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