A cheatsheet for me, since I will forget which underscore does what and which fence wants a language tag. Most of this is plain Markdown plus the extras from pymdown-extensions listed in blog/templatetags/markdown_extras.py.

Inline and display math

Inline with single dollars, display with doubles. Underscores inside math do not trigger italic.

$\mathfrak{sl}_2 = \operatorname{span}\{E, F, H\}$

$$[H, E] = 2E, \quad [H, F] = -2F, \quad [E, F] = H$$

Renders as \(\mathfrak{sl}_2 = \operatorname{span}\{E, F, H\}\), then

AMS environments live inside $$ ... $$:

$$
\begin{align}
\Delta(E) &= E \otimes 1 + K \otimes E \\
\Delta(F) &= F \otimes K^{-1} + 1 \otimes F
\end{align}
$$

cases, pmatrix, bmatrix, array, and so on all work the same way. Equation tags are AMS-style (config in base.html).

Headings

## H2 and ### H3 for sections inside the body. The post title already occupies # H1, so do not use that level.

Lists

- one item
- another
  - sub-item by indent

1. first
2. second

• one item
• another

• sub-item by indent

• first

• second

Code blocks

Fence with a language tag and Pygments picks it up:

```julia
function bracket(L, A)
    sum(s -> A^(a(s) - b(s)) * (-A^2 - A^-2)^(loops(s) - 1), states(L))
end
```

function bracket(L, A)
    sum(s -> A^(a(s) - b(s)) * (-A^2 - A^-2)^(loops(s) - 1), states(L))
end

Inline code with single backticks: using LinearAlgebra.

Tables

| Generator | Action                                  |
|-----------|-----------------------------------------|
| $E$       | raises weight by two                    |
| $F$       | lowers weight by two                    |
| $H$       | diagonal, eigenvalues are the weights   |

Blockquotes

The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.

(Wigner, The Unreasonable Effectiveness of Mathematics in the Natural Sciences)

Footnotes

Drop [^name] inline, define at the bottom:

The bracket polynomial[^kauffman] is a state sum over crossings.

[^kauffman]: Kauffman, *On Knots*, Princeton, 1987.

Emphasis

*italic*, **bold**, ~~strikethrough~~ give italic, bold, strikethrough.

Links

[Anathem](https://www.nealstephenson.com/anathem.html) becomes Anathem. Bare URLs are linkified automatically.

Embedding a Pluto notebook

Raw HTML is allowed in the body:

<iframe src="/static/blog/notebooks/<slug>.html" class="notebook-embed" loading="lazy"></iframe>

The .notebook-embed class is theme-aware. Export with bin/export-to-blog from ~/Projects/julia-math/.

Smart symbols

-> becomes →, <- becomes ←, (c) becomes ©, +/- becomes ±. Inside math mode the proper TeX commands (\to, \copyright, \pm) are more precise; the smart-symbol pass mostly helps in prose.

What not to do

• No $math$ in titles. Titles flow into <title> and feed metadata, neither of which run MathJax.
• No AMS environments outside $$ ... $$. They need math mode.
• No heredocs when seeding posts from bash. Bash eats backslashes and \frac becomes rac. Drop the script into scripts/ and run python manage.py shell < scripts/foo.py.
• No raw HTML for math. The dollar delimiters are enough and MathJax catches them at render time.

This guide was drafted by Claude (Anthropic) at my request, as a working example of a Fragment and a permanent reference for myself. Edits and additions are my own as I go.