[{"data":1,"prerenderedAt":95},["ShallowReactive",2],{"article-markdown-latex":3,"i-lucide:box":30,"i-lucide:code-2":35,"i-lucide:file-text":37,"i-lucide:image":39,"i-lucide:square-sigma":41,"i-lucide:gamepad-2":43,"i-lucide:sparkles":45,"i-lucide:menu":47,"i-lucide:moon":49,"i-lucide:sun":51,"i-material-symbols:language":53,"i-lucide:chevron-down":55,"i-lucide:check":57,"i-lucide:check-circle":59,"i-lucide:download":61,"i-lucide:sigma":63,"i-lucide:copy":65,"i-lucide:trash-2":67,"i-lucide:layout-template":69,"i-lucide:calculator":71,"i-lucide:book":73,"i-lucide:file-check":75,"i-lucide:shield":77,"i-lucide:clipboard-paste":79,"i-lucide:eye":81,"i-lucide:pen-line":83,"i-lucide:file-code-2":85,"i-lucide:share-2":88,"i-lucide:git-branch":90,"i-lucide:arrow-up-right":92,"i-lucide:film":94,"i-lucide:graduation-cap":94,"i-tabler:markdown":94},{"zh":4,"en":17},[5,8,11,14],{"title":6,"content":7},"在线 LaTeX 公式编辑器：实时预览、快捷输入与一键导出","\u003Cp>MeTool 的 LaTeX 公式编辑器将\u003Cstrong>代码编辑、实时渲染、快捷符号插入、图片导出\u003C\u002Fstrong>整合在一个页面。无需安装 TeX 发行版或任何桌面软件，打开浏览器即可使用。\u003C\u002Fp>\u003Cp>工具分为上下两区：上方是预览区，公式渲染结果随输入实时更新；下方是编辑区，左侧为带语法高亮的 LaTeX 代码编辑器（基于 CodeMirror 6），右侧是按分类整理的快捷符号面板——希腊字母、运算符、上下标、分数根式、求和积分、矩阵模板等，点击即插入，避免手敲 \u003Ccode>\\alpha\u003C\u002Fcode>、\u003Ccode>\\frac{}{}\u003C\u002Fcode> 这类长命令。\u003C\u002Fp>\u003Cp>渲染引擎选用 KaTeX（Khan Academy 开源）。KaTeX 是目前最快的浏览器端 LaTeX 渲染方案，支持微积分、线性代数、概率统计、电磁学等绝大多数理工科数学场景。\u003Cstrong>所有渲染均在本地完成，公式内容不会上传任何服务器。\u003C\u002Fstrong>\u003C\u002Fp>",{"title":9,"content":10},"LaTeX 公式语法速查","\u003Ch3>上下标\u003C\u002Fh3>\u003Cul>\u003Cli>上标：\u003Ccode>x^2\u003C\u002Fcode>，多字符：\u003Ccode>x^{n+1}\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>下标：\u003Ccode>x_i\u003C\u002Fcode>，多字符：\u003Ccode>x_{ij}\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>同时：\u003Ccode>x_i^2\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>分数与根号\u003C\u002Fh3>\u003Cul>\u003Cli>分数：\u003Ccode>\\frac{a}{b}\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>平方根：\u003Ccode>\\sqrt{x}\u003C\u002Fcode>；n 次方根：\u003Ccode>\\sqrt[n]{x}\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>求和、积分、极限\u003C\u002Fh3>\u003Cul>\u003Cli>求和：\u003Ccode>\\sum_{i=0}^{n} i^2\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>积分：\u003Ccode>\\int_a^b f(x)\\,dx\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>极限：\u003Ccode>\\lim_{x \\to 0} \\frac{\\sin x}{x}\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>矩阵\u003C\u002Fh3>\u003Cpre>\u003Ccode>\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}\u003C\u002Fcode>\u003C\u002Fpre>\u003Cp>\u003Ccode>pmatrix\u003C\u002Fcode>（圆括号）、\u003Ccode>bmatrix\u003C\u002Fcode>（方括号）、\u003Ccode>vmatrix\u003C\u002Fcode>（行列式竖线）、\u003Ccode>cases\u003C\u002Fcode>（分段函数）。\u003C\u002Fp>\u003Ch3>多行对齐公式\u003C\u002Fh3>\u003Cpre>\u003Ccode>\\begin{aligned}\n  a &= b + c \\\\\n  d &= e + f\n\\end{aligned}\u003C\u002Fcode>\u003C\u002Fpre>\u003Cp>\u003Ccode>&\u003C\u002Fcode> 是对齐锚点，\u003Ccode>\\\\\u003C\u002Fcode> 换行，\u003Ccode>[4pt]\u003C\u002Fcode> 可调行间距。\u003C\u002Fp>\u003Ch3>常用希腊字母\u003C\u002Fh3>\u003Cp>\u003Ccode>\\alpha \\beta \\gamma \\delta \\theta \\lambda \\mu \\pi \\sigma \\omega \\Sigma \\Omega \\nabla \\partial\u003C\u002Fcode>\u003C\u002Fp>",{"title":12,"content":13},"快捷符号面板的使用技巧","\u003Cp>符号面板分为两个 Tab：\u003Cstrong>快捷符号\u003C\u002Fstrong>和\u003Cstrong>公式模板\u003C\u002Fstrong>。\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>快捷符号\u003C\u002Fstrong>：希腊字母（α β γ…）、运算符（± × ÷ ≤ ≥ ∈ ∇ ∂…）、上下标标注（x² xₙ x̄ x̂ ẋ…），点击后命令直接追加到光标位置。\u003C\u002Fli>\u003Cli>\u003Cstrong>公式模板\u003C\u002Fstrong>：\u003Ccode>\\frac{}{}\u003C\u002Fcode>（分数）、\u003Ccode>\\sqrt{}\u003C\u002Fcode>（根号）、\u003Ccode>\\sum_{i=0}^{n}\u003C\u002Fcode>（求和）、\u003Ccode>\\int_{a}^{b}\u003C\u002Fcode>（积分）、矩阵、行列式、分段函数、对齐环境等复合结构，点击后光标自动定位到第一个需要填写的参数位置。\u003C\u002Fli>\u003C\u002Ful>\u003Cp>移动端支持 Tab 切换：默认显示代码区，切换到符号面板点选后自动跳回代码区，方便查看代码更新。桌面端两侧始终并排显示。\u003C\u002Fp>",{"title":15,"content":16},"LaTeX 公式导出为图片：适配各平台的最佳方案","\u003Cp>微信公众号、PPT、Word、飞书文档等平台不支持直接渲染 LaTeX，最通用的解决方案是导出为图片后插入。本工具提供三种导出格式：\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>PNG（高清 2×）\u003C\u002Fstrong>：适合 Word 文档、微信截图、社交媒体发布。导出尺寸是屏幕像素的 2 倍，在 Retina \u002F 高 DPI 屏幕上清晰无锯齿。\u003C\u002Fli>\u003Cli>\u003Cstrong>SVG（矢量）\u003C\u002Fstrong>：适合 PPT、设计稿（Figma \u002F Sketch）、技术博客。无限缩放不失真，文件体积小，嵌入 HTML 时可直接用 CSS 控制大小。\u003C\u002Fli>\u003Cli>\u003Cstrong>复制 LaTeX 源码\u003C\u002Fstrong>：适合 GitHub、Notion、Obsidian、Jupyter Notebook、Typora 等原生支持 LaTeX 的平台。行内公式用 \u003Ccode>$...$\u003C\u002Fcode> 包裹，块级公式用 \u003Ccode>$$...$$\u003C\u002Fcode>，点击 \u003Cstrong>$…$\u003C\u002Fstrong> 按钮可自动添加分隔符。\u003C\u002Fli>\u003C\u002Ful>\u003Cp>导出图片时，无论当前界面是亮色还是暗色主题，输出均为白色背景 + 黑色公式，方便直接放入白底文档。\u003C\u002Fp>",[18,21,24,27],{"title":19,"content":20},"Online LaTeX Formula Editor: Real-time Preview, Quick Insert & One-click Export","\u003Cp>MeTool's LaTeX formula editor combines \u003Cstrong>code editing, live rendering, quick symbol insertion, and image export\u003C\u002Fstrong> in a single page — no TeX distribution or desktop software required.\u003C\u002Fp>\u003Cp>The layout is split into two sections: the preview area at the top renders your formula in real time as you type; the editor area below has a LaTeX code editor (CodeMirror 6 with syntax highlighting) on the left and a categorised symbol panel on the right — Greek letters, operators, sub\u002Fsuperscripts, fractions, summation, integrals, matrix templates and more, all inserted on click.\u003C\u002Fp>\u003Cp>Rendering is powered by KaTeX (open-sourced by Khan Academy), the fastest in-browser LaTeX rendering solution available. It covers calculus, linear algebra, probability, electromagnetism and virtually all undergraduate-to-graduate STEM mathematics. \u003Cstrong>All rendering happens locally — your formulas never leave your device.\u003C\u002Fstrong>\u003C\u002Fp>",{"title":22,"content":23},"LaTeX Formula Syntax Quick Reference","\u003Ch3>Subscripts & Superscripts\u003C\u002Fh3>\u003Cul>\u003Cli>Superscript: \u003Ccode>x^2\u003C\u002Fcode>; multi-char: \u003Ccode>x^{n+1}\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>Subscript: \u003Ccode>x_i\u003C\u002Fcode>; multi-char: \u003Ccode>x_{ij}\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>Fractions & Roots\u003C\u002Fh3>\u003Cul>\u003Cli>Fraction: \u003Ccode>\\frac{a}{b}\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>Square root: \u003Ccode>\\sqrt{x}\u003C\u002Fcode>; nth root: \u003Ccode>\\sqrt[n]{x}\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>Summation, Integrals & Limits\u003C\u002Fh3>\u003Cul>\u003Cli>Sum: \u003Ccode>\\sum_{i=0}^{n} i^2\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>Integral: \u003Ccode>\\int_a^b f(x)\\,dx\u003C\u002Fcode>\u003C\u002Fli>\u003Cli>Limit: \u003Ccode>\\lim_{x \\to 0} \\frac{\\sin x}{x}\u003C\u002Fcode>\u003C\u002Fli>\u003C\u002Ful>\u003Ch3>Matrices\u003C\u002Fh3>\u003Cpre>\u003Ccode>\\begin{pmatrix} a & b \\\\ c & d \\end{pmatrix}\u003C\u002Fcode>\u003C\u002Fpre>\u003Cp>\u003Ccode>pmatrix\u003C\u002Fcode> (parens), \u003Ccode>bmatrix\u003C\u002Fcode> (brackets), \u003Ccode>vmatrix\u003C\u002Fcode> (determinant bars), \u003Ccode>cases\u003C\u002Fcode> (piecewise functions).\u003C\u002Fp>\u003Ch3>Multi-line Aligned Equations\u003C\u002Fh3>\u003Cpre>\u003Ccode>\\begin{aligned}\n  a &= b + c \\\\\n  d &= e + f\n\\end{aligned}\u003C\u002Fcode>\u003C\u002Fpre>\u003Cp>\u003Ccode>&\u003C\u002Fcode> is the alignment anchor; \u003Ccode>\\\\\u003C\u002Fcode> breaks the line; \u003Ccode>[4pt]\u003C\u002Fcode> increases row spacing.\u003C\u002Fp>\u003Ch3>Common Greek Letters\u003C\u002Fh3>\u003Cp>\u003Ccode>\\alpha \\beta \\gamma \\delta \\theta \\lambda \\mu \\pi \\sigma \\omega \\Sigma \\Omega \\nabla \\partial\u003C\u002Fcode>\u003C\u002Fp>",{"title":25,"content":26},"Using the Quick-Insert Symbol Panel","\u003Cp>The symbol panel has two tabs: \u003Cstrong>Symbols\u003C\u002Fstrong> and \u003Cstrong>Templates\u003C\u002Fstrong>.\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>Symbols\u003C\u002Fstrong>: Greek letters (α β γ…), operators (± × ÷ ≤ ≥ ∈ ∇ ∂…), accent marks (x̄ x̂ ẋ…) — click inserts the command at the cursor.\u003C\u002Fli>\u003Cli>\u003Cstrong>Templates\u003C\u002Fstrong>: \u003Ccode>\\frac{}{}\u003C\u002Fcode>, \u003Ccode>\\sqrt{}\u003C\u002Fcode>, \u003Ccode>\\sum_{i=0}^{n}\u003C\u002Fcode>, \u003Ccode>\\int_{a}^{b}\u003C\u002Fcode>, matrix, determinant, piecewise function, aligned environment — composite structures where the cursor jumps to the first parameter after insertion.\u003C\u002Fli>\u003C\u002Ful>\u003Cp>On mobile, the editor and symbol panel are on separate tabs. Switching to the symbol panel, clicking an item, then automatically returns you to the code tab so you can see the updated code immediately.\u003C\u002Fp>",{"title":28,"content":29},"Exporting LaTeX Formulas as Images: Platform-by-Platform Guide","\u003Cp>WeChat articles, PowerPoint, Word, and many other platforms can't render LaTeX directly. The universal workaround is exporting as an image. Three export formats are available:\u003C\u002Fp>\u003Cul>\u003Cli>\u003Cstrong>PNG (2× HiDPI)\u003C\u002Fstrong>: for Word documents, WeChat screenshots, and social media. Output is 2× the screen pixels, crisp on Retina and high-DPI displays.\u003C\u002Fli>\u003Cli>\u003Cstrong>SVG (vector)\u003C\u002Fstrong>: for PowerPoint, Figma\u002FSketch, and technical blogs. Infinitely scalable, small file size, and can be sized with CSS when embedded in HTML.\u003C\u002Fli>\u003Cli>\u003Cstrong>Copy LaTeX source\u003C\u002Fstrong>: for platforms with native LaTeX support — GitHub (README, Issues), Notion, Obsidian, Jupyter Notebook, Typora. 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