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refact: eliminate blog/docs content overlap

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- Delete blog/copy-math-to-word (EN+ZH) — identical to docs/copy-to-word
- Rewrite blog/pdf-formula-issues as narrative troubleshooting story;
  operational steps now link out to docs/pdf-extraction
- Add "Further reading" cross-links: 4 docs → relevant blog posts
- Add "See also" cross-links: 3 blog posts → relevant docs

Docs = product reference; Blog = narrative/use cases/opinions

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>
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yoge
2026-03-26 16:52:27 +08:00
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Over a semester, you'll accumulate dozens of recognized formulas. Consider organizing them: paste each into a reference `.tex` file with a short comment. By exam time, you'll have a searchable personal formula sheet that took almost no effort to build.
**See also:** For supported file types, size limits, and copy options, see the [Image to LaTeX documentation →](/docs/image-to-latex)
[Start digitizing your notes →](/app)

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---
title: "Why Your PDF Formulas Come Out Wrong (and How to Fix It)"
description: The most common reasons PDF formula extraction produces errors, and exactly how to fix each one
title: "I Tried to Extract Formulas from My Professor's PDF. Here's What I Learned."
description: A real-world account of what goes wrong with PDF formula extraction — and why most problems come down to one of three root causes
slug: pdf-formula-issues
date: 2026-02-15
tags: [troubleshooting, PDF, tips]
tags: [troubleshooting, PDF]
---
# Why Your PDF Formulas Come Out Wrong (and How to Fix It)
# I Tried to Extract Formulas from My Professor's PDF. Here's What I Learned.
PDF formula extraction should be simple — upload, get LaTeX, done. But sometimes the output looks garbled, symbols are missing, or the extractor says no formulas were found. Here's a breakdown of the most common causes and how to fix each one.
Last semester I was working through a 200-page lecture notes PDF — the kind that gets scanned from printed transparencies, emailed as a file attachment, and opens with a slightly-off angle on every page. I wanted to pull the key equations into my own notes. What followed was an education in how PDFs actually store (or don't store) mathematical content.
## Problem 1: The PDF is a Scan
## The First Surprise: Not All PDFs Are the Same
**Symptoms:** Symbols look correct on screen but extraction output is garbage or empty.
I naively assumed "PDF with formulas" meant "formulas I can extract." Not true.
**Why it happens:** A scanned PDF is just a collection of images — there's no actual text layer. The text you see in your PDF reader is either from OCR performed at scan time (often poor quality) or from the image itself.
There are at least three fundamentally different kinds of PDFs floating around in academic circles, and they behave completely differently:
**Fix:** Run TexPixel's image-based pipeline instead. Export individual pages as PNG at 300 DPI using any PDF viewer (File → Export as Image in Preview, or Adobe Acrobat's Export PDF feature), then upload the PNG directly. Image-based recognition handles scans correctly; direct PDF text extraction does not.
**Born-digital PDFs** (generated from LaTeX, Word, or typesetting software) contain actual vector math. Extraction from these is fast and 95%+ accurate — the formula structure is essentially already there.
## Problem 2: Low-DPI Scan
**Scanned PDFs** are just photographs of printed pages packaged into a container. There's no text layer. Extraction works through image recognition, and accuracy depends entirely on scan quality. My professor's notes were this kind.
**Symptoms:** Some symbols recognized correctly, others replaced with wrong characters or dropped entirely.
**Hybrid PDFs** have a text layer added by OCR software after scanning. Quality varies wildly — sometimes great, sometimes the "text" layer is completely wrong. These are the most unpredictable.
**Why it happens:** Below about 150 DPI, strokes in small symbols like `\prime`, `\cdot`, or subscript characters become a few pixels wide — too blurry to reliably distinguish.
## The Three Root Causes of Most Failures
**Fix:** Rescan at 300 DPI. Most modern flatbed scanners default to 200 DPI; bumping to 300 produces dramatically better results without significantly increasing file size. For phone scans, use a dedicated scanner app (e.g., Adobe Scan, Microsoft Lens) which applies automatic sharpening and perspective correction.
After a lot of trial and error, I found that failed extractions almost always come back to one of three things:
## Problem 3: Password-Protected PDF
**1. Resolution.** The scan was done at 150 DPI instead of 300. At low resolution, small symbols — subscripts, primes, dots — become a few pixels wide. The model can't reliably distinguish `\prime` from a stray speck. Rescanning at 300 DPI fixed more than half my problems.
**Symptoms:** "No formulas found" or upload fails entirely.
**2. Encryption.** Some PDFs are password-protected or have content restrictions that prevent any tool from reading the content stream. The PDF appears to open fine, but nothing can extract from it. Removing the password (File → Export as PDF in Preview, without the password lock) solved this.
**Why it happens:** Encrypted PDFs require a password to access their content stream. TexPixel cannot process the content of a locked file.
**3. Formulas stored as vector paths.** Some PDF generators draw equations as shapes rather than encoding them as characters. To any extraction tool, these formulas are invisible — just abstract geometry. The only way around this is to render the page as an image and run visual recognition on that instead.
**Fix:** Remove the password protection before uploading. In Preview (Mac), open with the password, then File → Export as PDF — the exported file won't have the password. In Adobe Reader, use File → Print → Save as PDF.
## What Actually Worked
## Problem 4: Formulas Stored as Vector Paths
For my professor's scanned notes, the workflow that worked:
**Symptoms:** PDF looks perfect, but extraction returns nothing or incorrect text.
1. Export each page as a 300 DPI PNG using Preview
2. Upload the PNG to TexPixel
3. Get clean LaTeX back in under a second
**Why it happens:** Some PDF generators (certain Word versions, some online LaTeX renderers) rasterize or vectorize math into paths — the formulas are essentially drawings, not characters. There's no character stream to extract.
Not the direct-PDF workflow I was hoping for, but reliable. The image-based pipeline doesn't care whether the original was scanned or born-digital — it just sees pixels and reads the math.
**Fix:** Export the page as a high-resolution PNG (300 DPI), then upload as an image. TexPixel's visual recognition pipeline handles vector-rendered formulas well.
## The Bigger Lesson
## Problem 5: Multi-Column Layout
PDF is a presentation format, not a data format. It's optimized for how things look, not for what they mean. Mathematical notation in particular gets mangled in transit — rendered, rasterized, path-converted — in ways that destroy the underlying structure.
**Symptoms:** Formulas from two columns are merged or interleaved in the output.
The most reliable signal is always the image. When in doubt, export to PNG and let visual recognition do the work.
**Why it happens:** PDF text streams don't always encode reading order correctly, especially in two-column academic papers.
---
**Fix:** Crop to a single column before uploading. Use any image editor to crop the page into left and right halves, then upload each separately.
## Problem 6: Handwritten Annotations
**Symptoms:** Handwritten notes over a printed formula confuse the output.
**Why it happens:** TexPixel sees both the printed formula and the handwritten annotations together. It may try to recognize the annotations as part of the formula.
**Fix:** Crop tightly to just the printed formula, excluding any handwriting around it.
## Quick Diagnostic Checklist
Before uploading a problematic PDF:
- [ ] Is it a scan or a born-digital PDF?
- [ ] If a scan, what DPI was it scanned at?
- [ ] Is it password-protected?
- [ ] Does it have a two-column layout?
- [ ] Are there handwritten annotations?
Working through this list resolves the issue 90% of the time.
[Upload your PDF →](/app)
For a systematic reference on PDF types, file limits, and what TexPixel can handle, see the [PDF Extraction documentation →](/docs/pdf-extraction)

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---
title: "Copy Math to Word Without Losing Formatting — The Right Way"
description: Three methods for getting recognized formulas into Microsoft Word, ranked by quality and effort
slug: copy-math-to-word
date: 2026-03-01
tags: [tutorial, Word, export]
---
# Copy Math to Word Without Losing Formatting — The Right Way
Most people's first instinct when they need a formula in a Word document is to take a screenshot. It works — until you need to resize the document, change the font, or edit the formula. Screenshots break. Native equations don't.
Here are three ways to get TexPixel's output into Word, from best to worst.
## Method 1: DOCX Export (Best)
The cleanest option. TexPixel converts your recognized formula into a native Word equation (OMML format) and packages it in a `.docx` file.
**How:**
1. Upload your formula image to TexPixel.
2. Click **Export** → select **DOCX**.
3. Open the downloaded file in Word.
4. Select the equation, copy, paste into your target document.
**Why it's best:** The formula is fully editable in Word's built-in equation editor. Double-click it to open the editor, change any symbol, resize it — it behaves exactly like an equation you typed yourself. It also scales correctly when you change font sizes.
**Limitation:** Each upload produces one `.docx` file. If you have many formulas to insert, you'll need to repeat the process or batch them (see below).
## Method 2: Paste LaTeX into Word's Equation Editor (Good)
Word 2019+ and Microsoft 365 support pasting LaTeX directly into equations.
**How:**
1. Get the LaTeX output from TexPixel (e.g., `x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}`).
2. In Word, insert a new equation: **Insert → Equation** (or press `Alt+=`).
3. Make sure the equation box is in **LaTeX mode** (click the dropdown on the right side of the equation box → select "LaTeX").
4. Paste the LaTeX string. Press **Enter** or click outside.
Word converts the LaTeX to a rendered, editable equation.
**Why it's good:** Fast for single formulas. No file download required.
**Limitation:** Word's LaTeX parser doesn't support all LaTeX commands. Obscure or complex expressions may not render correctly. Test before relying on it for important documents.
## Method 3: Image Export (Worst, But Sometimes Necessary)
Export the formula as a PNG and insert it as an image in Word.
**When to use:** Only when you need the formula in a document being shared with someone who doesn't have Word's equation editor (e.g., older Word versions, third-party editors). Or when a complex formula doesn't render correctly via Methods 1 or 2.
**Downsides:** Not editable. Doesn't scale well. Accessibility tools can't read it.
## Handling Multiple Formulas
If you have many formulas to insert into a single document:
1. Upload each formula image and collect the LaTeX strings.
2. Open a new Word document.
3. For each formula, use the **Alt+=** method above to insert them in sequence.
4. Once all formulas are inserted, copy and paste the entire equation block into your target document.
This is faster than one DOCX export per formula.
## Google Docs
Google Docs doesn't natively support LaTeX paste. Options:
- Use the **Auto-LaTeX Equations** Google Docs add-on, which renders LaTeX strings as inline images.
- Export as DOCX and open in Google Docs (equations import as images, not editable).
- Use a tool like `mathpix-markdown-it` to convert to Markdown and render in a Markdown-compatible environment.
For serious equation-heavy work, Word or Overleaf remain better choices than Google Docs.
[Export your next formula to Word →](/app)

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Start with the past year's notebooks. The 7-hour investment pays dividends for years.
**See also:** For PDF file limits, supported types, and export options, see the [PDF Extraction documentation →](/docs/pdf-extraction)
[Start digitizing your notes →](/app)

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---
With these habits, you'll see noticeably better accuracy — often 95%+ even for complex handwritten expressions.
**See also:** For a systematic breakdown of what affects accuracy (DPI, contrast, formula complexity), see the [OCR Accuracy documentation →](/docs/ocr-accuracy)

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一个学期下来，你会积累几十个识别出的公式。不妨整理一下：将每个公式粘贴到一个参考 `.tex` 文件中，加上简短注释。期末时，你将拥有一份几乎不费力气就建立起来的、可搜索的个人公式表。
**参考文档：** 关于支持的文件类型、大小限制和复制选项，请查看 [图片转 LaTeX 文档 →](/docs/image-to-latex)
[开始数字化你的笔记 →](/app)

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---
title: "PDF 公式识别出错的原因及修复方法"
description: PDF 公式提取产生错误最常见的原因，以及每种情况的具体解决方案
title: "我试着从教授的 PDF 里提取公式，结果学到了这些"
description: 一次真实的 PDF 公式提取经历——以及为什么大多数问题都归结为三个根本原因
slug: pdf-formula-issues
date: 2026-02-15
tags: [故障排查, PDF, 技巧]
tags: [故障排查, PDF]
---
# PDF 公式识别出错的原因及修复方法
# 我试着从教授的 PDF 里提取公式，结果学到了这些
PDF 公式提取本应简单——上传、得到 LaTeX、完成。但有时输出乱码、符号丢失，或者提示没有找到公式。以下是最常见原因的分析及对应的修复方法。
上学期我在啃一份 200 页的讲义 PDF——那种从印刷胶片扫描而来、作为附件发出来、每页都略微倾斜的类型。我想把关键方程提取到自己的笔记里。接下来发生的事，让我深刻理解了 PDF 究竟是怎么存储（或者说不存储）数学内容的。
## 问题 1：PDF 是扫描件
## 第一个意外：不是所有 PDF 都一样
**症状：** 屏幕上公式显示正确，但提取输出是乱码或空白。
我天真地以为"有公式的 PDF"就意味着"可以提取的公式"。并非如此。
**原因：** 扫描 PDF 实际上只是一组图片——没有真正的文字层。你在 PDF 阅读器中看到的文字，要么来自扫描时进行的 OCR（往往质量较差），要么直接来自图像本身。
学术圈里流传着至少三种根本不同的 PDF，它们的行为完全不同：
**解决方法：** 使用 TexPixel 的图像识别流程。用任意 PDF 查看器将页面导出为 300 DPI 的 PNG（Preview 中选择"文件 → 导出为图像"，或 Adobe Acrobat 的"导出 PDF"功能），然后直接上传 PNG。图像识别能正确处理扫描件；直接提取 PDF 文字则不行。
**数字原生 PDF**（由 LaTeX、Word 或排版软件生成）包含真正的矢量数学内容。从这类 PDF 提取速度快、准确率 95% 以上——公式结构本质上已经在那里了。
## 问题 2：扫描分辨率过低
**扫描 PDF** 只是打印页面的照片，被包装进一个容器。没有文字层。提取依赖图像识别，准确率完全取决于扫描质量。教授的讲义就是这种。
**症状：** 部分符号识别正确，其他符号被替换为错误字符或直接丢失。
**混合 PDF** 是扫描后由 OCR 软件添加文字层的 PDF。质量参差不齐——有时很好，有时"文字层"完全是错的。这类 PDF 最难预测。
**原因：** 低于约 150 DPI 时，`\prime`、`\cdot` 或下标字符等小符号的笔画只有几个像素宽——模糊到无法可靠区分。
## 大多数失败的三个根本原因
**解决方法：** 以 300 DPI 重新扫描。大多数平板扫描仪默认 200 DPI；提高到 300 DPI 能显著改善效果，且文件大小增加不大。对于手机扫描，使用专用扫描 App（如 Adobe Scan、Microsoft Lens）——这些 App 会自动锐化并进行透视校正。
经过大量尝试和失败，我发现提取失败几乎总是归结为以下三种情况之一：
## 问题 3：PDF 有密码保护
**1. 分辨率。** 扫描时用了 150 DPI 而不是 300 DPI。低分辨率下，小符号——下标、撇号、点——只有几个像素宽。模型无法可靠区分 `\prime` 和一个杂散的污点。提高到 300 DPI 重新扫描，解决了一半以上的问题。
**症状：** 显示"未找到公式"或上传完全失败。
**2. 加密。** 部分 PDF 有密码保护或内容限制，阻止任何工具读取内容流。PDF 看起来打开正常，但没有工具能从中提取。移除密码（在 Preview 中选择"文件 → 导出为 PDF"，不勾选密码锁）解决了这个问题。
**原因：** 加密 PDF 需要密码才能访问内容流。TexPixel 无法处理加密文件的内容。
**3. 公式存储为矢量路径。** 部分 PDF 生成器将方程绘制为图形而非编码为字符。对任何提取工具来说，这些公式是隐形的——只是抽象的几何图形。唯一的办法是将页面渲染为图像，然后对图像进行视觉识别。
**解决方法：** 上传前移除密码保护。在 Mac 的 Preview 中，用密码打开后，选择"文件 → 导出为 PDF"——导出的文件不含密码。在 Adobe Reader 中，使用"文件 → 打印 → 存储为 PDF"。
## 最终有效的方法
## 问题 4：公式存储为矢量路径
对于教授的扫描讲义，有效的工作流是：
**症状：** PDF 显示完美，但提取结果为空或不正确。
1. 用 Preview 将每页导出为 300 DPI PNG
2. 将 PNG 上传到 TexPixel
3. 不到一秒得到干净的 LaTeX
**原因：** 某些 PDF 生成器（特定版本的 Word、部分在线 LaTeX 渲染器）会将数学公式光栅化或矢量化为路径——公式本质上是图形，而非字符，没有字符流可以提取。
不是我期望的直接处理 PDF 的工作流，但很可靠。图像识别流程不在乎原文件是扫描的还是数字原生的——它只看像素，读取数学内容。
**解决方法：** 将页面导出为高分辨率 PNG（300 DPI），然后作为图像上传。TexPixel 的视觉识别流程能很好地处理矢量渲染的公式。
## 更大的启示
## 问题 5：双栏排版
PDF 是展示格式，不是数据格式。它针对外观进行了优化，而不是含义。数学符号在传输过程中尤其容易被损坏——渲染、光栅化、路径转换——以破坏底层结构的方式。
**症状：** 两栏的公式在输出中被合并或交叉混排。
最可靠的信号永远是图像。如果不确定，导出为 PNG，让视觉识别来完成工作。
**原因：** PDF 文字流并不总是以正确的阅读顺序编码，在双栏学术论文中尤为如此。
---
**解决方法：** 上传前裁剪为单栏。用任意图像编辑器将页面裁成左右两半，分别上传。
## 问题 6：手写批注
**症状：** 印刷公式上的手写笔记干扰输出。
**原因：** TexPixel 同时看到了印刷公式和手写批注，可能会尝试将批注识别为公式的一部分。
**解决方法：** 紧密裁剪，只保留印刷公式部分，排除周围的手写内容。
## 快速排查清单
上传有问题的 PDF 之前，先检查：
- [ ] 是扫描件还是数字原生 PDF？
- [ ] 如果是扫描件，分辨率是多少 DPI？
- [ ] 是否有密码保护？
- [ ] 是否是双栏排版？
- [ ] 是否有手写批注？
逐项排查，能解决 90% 的问题。
[上传你的 PDF →](/app)
关于 PDF 类型、文件限制以及 TexPixel 支持范围的系统性参考，请查看 [PDF 公式提取文档 →](/docs/pdf-extraction)

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---
title: "把公式粘贴到 Word 而不丢失格式——正确的方法"
description: 三种将识别公式导入 Microsoft Word 的方法，按质量和操作难度排序
slug: copy-math-to-word
date: 2026-03-01
tags: [教程, Word, 导出]
---
# 把公式粘贴到 Word 而不丢失格式——正确的方法
大多数人的第一反应是截图。这能用——直到你需要调整文档大小、更改字体或编辑公式。截图会出问题，原生方程式不会。
以下是三种将 TexPixel 输出导入 Word 的方法，从最好到最差排序。
## 方法 1：DOCX 导出（最佳）
最干净的选项。TexPixel 将识别的公式转换为原生 Word 方程式（OMML 格式），并打包到 `.docx` 文件中。
**操作步骤：**
1. 上传公式图片到 TexPixel
2. 点击**导出** → 选择 **DOCX**
3. 在 Word 中打开下载的文件
4. 选中方程式，复制，粘贴到目标文档
**为什么最好：** 公式在 Word 内置方程式编辑器中完全可编辑。双击打开编辑器，修改任意符号、调整大小——行为和你自己输入的方程式完全一样。更改字体大小时也能正确缩放。
**限制：** 每次上传生成一个 `.docx` 文件。如果有很多公式需要插入，需要重复操作或批量处理。
## 方法 2：将 LaTeX 粘贴到 Word 方程式编辑器（较好）
Word 2019+ 和 Microsoft 365 支持直接在方程式框中粘贴 LaTeX。
**操作步骤：**
1. 从 TexPixel 获取 LaTeX 输出（例如：`x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}`）
2. 在 Word 中插入新方程式：**插入 → 公式**（或按 `Alt+=`）
3. 确保方程式框处于 **LaTeX 模式**（点击方程式框右侧下拉菜单 → 选择"LaTeX"）
4. 粘贴 LaTeX 字符串，按**回车**或点击外部
Word 会将 LaTeX 转换为可渲染、可编辑的方程式。
**为什么较好：** 单个公式处理很快，无需下载文件。
**限制：** Word 的 LaTeX 解析器不支持所有 LaTeX 命令。复杂或不常见的表达式可能无法正确渲染。用于重要文档前请先测试。
## 方法 3：图片导出（最差，但有时必要）
将公式导出为 PNG，在 Word 中作为图片插入。
**何时使用：** 仅在需要与没有 Word 方程式编辑器的用户共享文档时使用（例如旧版 Word、第三方编辑器），或当复杂公式通过方法 1 和 2 无法正确渲染时。
**缺点：** 不可编辑，缩放效果差，辅助工具无法读取。
## 处理多个公式
如果需要在一个文档中插入多个公式：
1. 上传每张公式图片，收集 LaTeX 字符串
2. 打开一个新 Word 文档
3. 对每个公式使用上面的 `Alt+=` 方法依次插入
4. 插入所有公式后，将整个方程式块复制粘贴到目标文档
这比每个公式单独导出 DOCX 更快。
## Google 文档
Google 文档不原生支持 LaTeX 粘贴。可选方案：
- 使用 **Auto-LaTeX Equations** Google 文档插件，将 LaTeX 字符串渲染为行内图片
- 导出为 DOCX 后在 Google 文档中打开（方程式以图片形式导入，不可编辑）
- 使用 `mathpix-markdown-it` 等工具转换为 Markdown，在支持 Markdown 的环境中渲染
对于大量包含公式的工作，Word 或 Overleaf 仍然是比 Google 文档更好的选择。
[导出你的下一个公式到 Word →](/app)

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从过去一年的笔记本开始。7 小时的投入，将带来多年的回报。
**参考文档：** 关于 PDF 文件限制、支持类型和导出选项，请查看 [PDF 公式提取文档 →](/docs/pdf-extraction)
[开始数字化你的笔记 →](/app)

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---
养成这些习惯后，你会发现识别准确率明显提升——即使是复杂的手写表达式也能达到 95% 以上。
**参考文档：** 关于影响准确率的系统性分析（分辨率、对比度、公式复杂度），请查看 [识别准确率文档 →](/docs/ocr-accuracy)

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**Further reading:** [LaTeX vs MathML: Which Format Should You Use? →](/blog/latex-vs-mathml)
[Try exporting a formula to Word →](/app)

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**Further reading:** [From Whiteboard to LaTeX in 3 Seconds: A Student's Workflow →](/blog/student-workflow)
Ready to try it? [Upload a formula image now →](/app)

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**Further reading:** [5 Tips for Better Handwriting Recognition →](/blog/handwriting-tips)
[Upload a formula and test accuracy →](/app)

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**Further reading:** [I tried to extract formulas from my professor's PDF — real-world troubleshooting →](/blog/pdf-formula-issues)
[Upload a PDF and extract formulas →](/app)

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**延伸阅读：** [LaTeX vs MathML：应该选哪种格式？→](/blog/latex-vs-mathml)
[尝试将公式导出到 Word →](/app)

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**延伸阅读：** [3 秒从白板到 LaTeX：学生的高效工作流 →](/blog/student-workflow)
准备好了吗？[立即上传公式图片 →](/app)

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**延伸阅读：** [提高手写公式识别准确率的 5 个技巧 →](/blog/handwriting-tips)
[上传公式测试识别准确率 →](/app)

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**延伸阅读：** [我试着从教授的 PDF 里提取公式——真实排障经历 →](/blog/pdf-formula-issues)
[上传 PDF 提取公式 →](/app)