文档具备完整的HTML、CSS和JavaScript功能。一个备注是一个HTML文件：其首行加载tern.js，其下方的所有内容均用Tern的语法编写，文件打开时会在原位渲染。

文献资料

文档发布于 ozkrac.github.io/tern。从指南开始。这些页面本身就是 Tern Notes：同样的文件在该仓库中是 index.html 和 [docs/，并且它们在浏览器中也能本地打开。

正在获得tern.js

一个音符只需 tern.js

一个附加组件也适用于标签，如data-use="addons/katex.js";两种形式协同工作。

来自jsDelivr，该软件为本仓库的标签发布提供：

• 要跟随发布， 使用 @1.1（最新的 1.1.x）、@1（最新的 1.x：大调保持每个音符的渲染相同）或 @latest（最新发布）。
• Not tern.min.js. jsDelivr 会根据请求进行任何文件的最小化，因此每个标签的 tern.min.js 会与 tern.js 并列，并在浏览器中生成注释;不要使用。工具和编辑只从名为 tern.js 的文件标签中获取笔记。在字节重要时，每个 GitHub 版本都会以该名携带一个缩小构建：“[https://github.

Luccet

Documents with the full power of HTML, CSS and JavaScript. A note is one HTML file: its first line loads luccet.js, and everything below it is written in Luccet’s syntax and rendered in place when the file is opened.

Luccet was called Tern until version 2.0. A note written for Tern needs its first line changed: see Migrating a note.

# Linear maps {#maps}

:::theorem[Rank–nullity]{#thm-rn}
If $V$ is finite-dimensional then $\dim V = \dim \ker T + \dim \operatorname{im} T$.
:::

By @thm-rn, an injective map between spaces of equal dimension is surjective.

It renders as plain HTML, in the browser’s own type and colours, light or dark, and the formulas as MathML: Luccet translates the TeX itself, with nothing to load (math). For a look, list a theme: ``.

Documentation

The documentation is published at luccet.dev. Start with the guide. The pages are themselves Luccet notes: the same files are index.html and docs/ in this repository, and they open locally in a browser too.

Getting luccet.js

A note needs only luccet.js

:::use
https://cdn.luccet.dev/themes/v1/classic.css
https://cdn.luccet.dev/code/v1/code.js
:::

One add-on also fits on the tag, as data-use="…/code.js"; both forms work together.

From cdn.luccet.dev, which serves every release from 2.0 on, minified:

• To follow releases, use v2.0/ (the newest 2.0.x) or v2/ (the newest 2.x: a major keeps every note rendering the same). A release’s own folder never changes, so a browser keeps its file for a year; a series’ or a major’s is checked for a newer release every hour.
• The same file is each GitHub Release’s luccet.js: the minified build, under the name the tools and the editors look for. Its luccet.css is beside it, for a page under a strict Content-Security-Policy.

Themes: colour themes after well-known palettes (Solarized, Gruvbox, Nord, Dracula, Catppuccin, Tokyo Night and more) live in their own repository, Luccet/themes. Each is an add-on: https://cdn.luccet.dev/themes/v1/nord.css in :::use (or data-use). See themes.