Math rendering reference

This post is the acceptance test for the math pipeline (FR-304). If anything below looks wrong, the build is broken.

Inline math

Euler’s identity $e^{i\pi} + 1 = 0$ sits inside a sentence. A vector $x \in \R^n$ uses the custom \R macro, and $\mathbb{E}[X] = \mu$ uses \mathbb. Fractions inline: $\frac{a}{b}$.

Display math

$$\int_{-\infty}^{\infty} e^{-x^2}\,dx = \sqrt{\pi}$$ $$\sum_{k=1}^{n} k = \frac{n(n+1)}{2}, \qquad \prod_{i=1}^{n} \left(1 + \frac{1}{i}\right) = n + 1$$

Aligned equations

$$\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}$$

Matrices

$$A = \begin{pmatrix} a_{11} & a_{12} & \cdots & a_{1n} \\ a_{21} & a_{22} & \cdots & a_{2n} \\ \vdots & \vdots & \ddots & \vdots \\ a_{m1} & a_{m2} & \cdots & a_{mn} \end{pmatrix}, \qquad \det \begin{bmatrix} a & b \\ c & d \end{bmatrix} = ad - bc$$

A very long equation

On a phone this should scroll sideways inside its own box, while the page itself stays put:

$$f(x) = a_0 + a_1 x + a_2 x^2 + a_3 x^3 + a_4 x^4 + a_5 x^5 + a_6 x^6 + a_7 x^7 + a_8 x^8 + a_9 x^9 + a_{10} x^{10} + a_{11} x^{11} + a_{12} x^{12}$$

Things that must not become math

• Price is $20, and another item costs $35.
• Inline code keeps dollars literal: echo $HOME and cost = $5.

# Code blocks are highlighted by Shiki (min-light), dollars untouched
price = "$20"
def mean(xs):
    return sum(xs) / len(xs)

Tables and footnotes (GFM)

Symbol	Meaning
$\R$	real numbers
$\nabla$	gradient

KaTeX runs at build time, so this page ships no math JavaScript.¹

Footnotes

1. Only the KaTeX stylesheet and fonts are loaded, and only on pages that contain math. ↩