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add Katex dependency, also a new article
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‎.gitignore‎

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Agents.md
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# Environment variables
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.env
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.env
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# VS code
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.vscode

‎app/docs/CommunityShare/Geek/CommonUsedMarkdown.md‎

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---
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title: 常用Markdown语法
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date: 2025-09-20 14:25:39
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---
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## 基础标题+字体样式
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`# 一级标题`
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`## 二级标题`
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以此类推
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**加粗字体** `**加粗字体**`
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_斜体字体_ `*斜体字体*`
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**_斜体加粗_** `***斜体加粗***`
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~~删除线~~ `~~删除线~~`
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<mark>荧光笔</mark> `<mark>荧光笔</mark>`
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半&ensp;角&ensp;空&ensp;格
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`半&ensp;角&ensp;空&ensp;格`
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全&emsp;角&emsp;空&emsp;格
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`全&emsp;角&emsp;空&emsp;格`
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## 无序、有序列表
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- 无序列表1&emsp;`* 无序列表1`
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- 无序列表2&emsp;`* 无序列表2`
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- 无序列表3&emsp;`* 无序列表3`
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- 无序列表4&emsp;`* 无序列表4`
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1. 有序列表1&emsp;`1. 有序列表1`
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2. 有序列表2&emsp;`2. 有序列表2`
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3. 有序列表3&emsp;`3. 有序列表3`
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4. 有序列表4&emsp;`4. 有序列表4`
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## 建表
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| 表头 | 左对齐 | 居中 | 右对齐 |
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| ------ | :----- | :----: | -----: |
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| 单元格 | 单元格 | 单元格 | 单元格 |
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| 单元格 | 单元格 | 单元格 | 单元格 |
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```
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| 表头 | 左对齐 | 居中 | 右对齐 |
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| - | :- | :-: | -: |
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| 单元格 | 单元格 | 单元格 | 单元格 |
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| 单元格 | 单元格 | 单元格 | 单元格 |
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```
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## 超链接
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`[想要显示的链接名](目标网址)`
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**示例**
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[点这里下载Anaconda](https://www.anaconda.com/download)
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`[点这里下载Anaconda](https://www.anaconda.com/download)`
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## 图片
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`![测试图片](./你的图片.jpg "自定义鼠标悬停显示名")`
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**示例**
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![测试图片](/CommonUsedMarkdown.assets/testpic1.jpg "autumn")
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`![测试图片](./CommonUsedMarkdown.assets/testpic1.jpg "autumn")`

‎app/docs/CommunityShare/Geek/Katex/Seb1.mdx‎

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---
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title: 个人常用字符
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date: 2025-09-20 14:25:39
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---
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## 希腊字母
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| 效果 | 指令 | 效果 | 指令 |
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| :--------: | :--------: | :-------: | :-------: |
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| $\alpha$ | `\alpha` | $\sigma$ | `\sigma` |
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| $\beta$ | `\beta` | $\tau$ | `\tau` |
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| $\gamma$ | `\gamma` | $\Gamma$ | `\Gamma` |
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| $\delta$ | `\delta` | $\Delta$ | `\Delta` |
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| $\epsilon$ | `\epsilon` | $\psi$ | `\psi` |
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| $\zeta$ | `\zeta` | $\omega$ | `\omega` |
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| $\eta$ | `\eta` | $\Omega$ | `\Omega` |
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| $\theta$ | `\theta` | $\Theta$ | `\Theta` |
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| $\lambda$ | `\lambda` | $\phi$ | `\phi` |
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| $\mu$ | `\mu` | $\varphi$ | `\varphi` |
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| $\pi$ | `\pi` | $\xi$ | `\xi` |
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| $\rho$ | `\rho` | | |
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## 箭头
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| 样例 | 指令 | 样例 | 指令 |
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| :---------------: | :---------------: | :------------------: | :------------------: |
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| $\leftarrow$ | `\leftarrow` | $\Leftarrow$ | `\Leftarrow` |
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| $\rightarrow$ | `\rightarrow` | $\Rightarrow$ | `\Rightarrow` |
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| $\leftrightarrow$ | `\leftrightarrow` | $\Leftrightarrow$ | `\Leftrightarrow` |
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| $\uparrow$ | `\uparrow` | $\mapsto$ | `\mapsto` |
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| $\downarrow$ | `\downarrow` | $\rightleftharpoons$ | `\rightleftharpoons` |
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## 运算符
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| 样例 | 指令 | 样例 | 指令 |
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| :------: | :------: | :-------: | :-------: |
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| $\times$ | `\times` | $\wedge$ | `\wedge` |
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| $\div$ | `\div` | $\vee$ | `\vee` |
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| $\cap$ | `\cap` | $\oplus$ | `\oplus` |
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| $\cup$ | `\cup` | $\otimes$ | `\otimes` |
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| $\cdot$ | `\cdot` | $\cdots$ | `\cdots` |
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## 关系符
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| 样例 | 指令 | 样例 | 指令 |
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| :-----: | :-----: | :---------: | :---------: |
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| $\neq$ | `\neq` | $\subset$ | `\subset` |
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| $\leq$ | `\leq` | $\subseteq$ | `\subseteq` |
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| $\geq$ | `\geq` | $\approx$ | `\approx` |
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| $\ll$ | `\ll` | $\equiv$ | `\equiv` |
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| $\gg$ | `\gg` | $\cong$ | `\cong` |
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| $\prec$ | `\prec` | $\parallel$ | `\parallel` |
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| $\succ$ | `\succ` | $\perp$ | `\perp` |
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| $\in$ | `\in` | $\notin$ | `\notin` |
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## 无穷、偏分、证明
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| 样例 | 指令 | 样例 | 指令 |
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| :-----------: | :-----------: | :----------: | :--------: |
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| $\infty$ | `\infty` | $\exists$ | `\exists` |
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| $\partial$ | `\partial` | $\neg$ | `\neg` |
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| $\varnothing$ | `\varnothing` | $\because$ | `\because` |
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| | $\therefore$ | `\therefore` |
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## 上标、下标
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| 样例 | 指令 | 样例 | 指令 |
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| :-----------------------: | :-----------------------: | :------------------------: | :------------------------: |
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| $\bar{a}$ | `\bar{a}` | | |
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| $\hat{a}$ | `\hat{a}` | | |
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| $\widehat{abc}$ | `\widehat{abc}` | | |
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| $\tilde{a}$ | `\tilde{a}` | $\utilde{a}$ | `\utilde{a}` |
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| $\widetilde{abc}$ | `\widetilde{abc}` | | |
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| $\vec{A}$ | `\vec{A}` | | |
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| $\overline{AB}$ | `\overline{AB}` | $\underline{AB}$ | `\underline{AB}` |
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| $\overleftarrow{AB}$ | `\overleftarrow{AB}` | $\underleftarrow{AB}$ | `\underleftarrow{AB}` |
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| $\overleftrightarrow{AB}$ | `\overleftrightarrow{AB}` | $\underleftrightarrow{AB}$ | `\underleftrightarrow{AB}` |
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| $\overleftharpoon{AB}$ | `\overleftharpoon{AB}` | | |
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| $\overgroup{AB}$ | `\overgroup{AB}` | $\undergroup{AB}$ | `\undergroup{AB}` |

‎app/docs/CommunityShare/Geek/Katex/Seb2.mdx‎

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---
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title: 数学公式语法
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date: 2025-09-20 14:25:39
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---
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## 矩阵、行列式
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$$
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\left(\begin{matrix}
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a & b \\
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c & d
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\end{matrix}\right)
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$$
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```latex
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$$
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\left(\begin{matrix}
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a & b \\
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c & d
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\end{matrix}\right)
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$$
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```
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$$
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\left|\begin{matrix}
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a & b \\
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c & d
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\end{matrix}\right|
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$$
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```latex
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$$
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\left|\begin{matrix}
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a & b \\
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c & d
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\end{matrix}\right|
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$$
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```
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$$
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\left(\begin{matrix}
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1 & 2 & \cdots & n \\
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2 & 3 & \cdots & n+1 \\
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\vdots & \vdots & \ddots & n^2 - 1\\
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n & n+1 & \cdots & n^2
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\end{matrix}\right)
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$$
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```latex
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$$
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\left(\begin{matrix}
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1 & 2 & \cdots & n \\
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2 & 3 & \cdots & n+1 \\
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\vdots & \vdots & \ddots & n^2 - 1\\
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n & n+1 & \cdots & n^2
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\end{matrix}\right)
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$$
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```
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## 维持等号缩进
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$$
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\begin{aligned}
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f(X|\theta) &= f(x_1,x_2,\cdots,x_n|\theta)\\
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&= f(x_1|\theta) \cdot f(x_2|\theta) \cdots f(x_n|\theta)\\
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&= \prod_{i=1}^n \frac{1}{x_i !} e^{-\theta}\theta^{x_i}\\
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&= \left(\prod_{i=1}^n \frac{1}{x_i !}\right) e^{-n \theta}\theta^{\sum_{i=1}^n x_i}
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\end{aligned}
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$$
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```latex
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$$
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\begin{aligned}
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f(X|\theta) &= f(x_1,x_2,\cdots,x_n|\theta)\\
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&= f(x_1|\theta) \cdot f(x_2|\theta) \cdots f(x_n|\theta)\\
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&= \prod_{i=1}^n \frac{1}{x_i !} e^{-\theta}\theta^{x_i}\\
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&= \left(\prod_{i=1}^n \frac{1}{x_i !}\right) e^{-n \theta}\theta^{\sum_{i=1}^n x_i}
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\end{aligned}
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$$
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```
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## 分段函数的表示（与Latex有差异）
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因为不能用`\equation`和各种`\cases`，所以需要变通一下
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$$
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f(x,\theta) = \left\{ \begin{array}{ll}
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\dfrac{1}{x\sqrt{2\pi \theta}} e^{-\frac{1}{2\theta} [\log(x)]^2} &,\text{ $x>0$} \\
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0 &,\text{ otherwise}
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\end{array} \right.
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$$
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```latex
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$$
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f(x,\theta) = \left\{ \begin{array}{ll}
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\dfrac{1}{x\sqrt{2\pi \theta}} e^{-\frac{1}{2\theta} [\log(x)]^2} &,\text{ $x>0$} \\
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0 &,\text{ otherwise}
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\end{array} \right.
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$$
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```

‎app/docs/CommunityShare/Geek/Katex/index.mdx‎

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---
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title: 常用Katex语法
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date: 2025-09-20 14:25:39
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---
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Katex 与 Latex 有些许的不同，稍作整理以便自己查阅
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在2个`$`之间增加指令，就可以实现行间数学模式，与正文不冲突
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在2个`$$`之间增加指令，将公式居中显示的单独模块

‎app/layout.tsx‎

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import { RootProvider } from "fumadocs-ui/provider";
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import Script from "next/script";
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import "./globals.css";
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import "katex/dist/katex.min.css";
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import { ThemeProvider } from "@/app/components/ThemeProvider";
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import { SpeedInsights } from "@vercel/speed-insights/next";
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‎next.config.mjs‎

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import { createMDX } from "fumadocs-mdx/next";
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import createNextIntlPlugin from "next-intl/plugin";
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const withMDX = createMDX();
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const withMDX = createMDX({
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configPath: "source.config.ts",
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});
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const withNextIntl = createNextIntlPlugin("./i18n.ts");
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/** @type {import('next').NextConfig} */

‎package.json‎

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"eslint": "^9.35.0",
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"eslint-config-next": "^15.5.3",
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"husky": "^9.1.7",
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"katex": "^0.16.22",
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"lint-staged": "^16.1.6",
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"postcss": "^8.5.6",
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"prettier": "3.6.2",
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"rehype-katex": "^7.0.1",
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"remark-math": "^6.0.0",
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"tailwindcss": "^4.1.13",
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"tw-animate-css": "^1.3.8",
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"typescript": "^5.6.3"

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