yn/test/md/math-katex.md

KaTeX Math Test

This document tests KaTeX math formula rendering in Yank Note.

Inline Math

The quadratic formula is x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}.

Einstein's equation: E = mc^2.

Simple expression: a^2 + b^2 = c^2.

Greek letters: \alpha, \beta, \gamma, \delta, \epsilon, \theta, \lambda, \mu, \pi, \sigma, \omega.

Block Math

\sum_{i=1}^{n} i = \frac{n(n+1)}{2}

\int_{0}^{\infty} e^{-x^2} dx = \frac{\sqrt{\pi}}{2}

f(x) = \begin{cases}
  x^2 & \text{if } x \geq 0 \\
  -x^2 & \text{if } x < 0
\end{cases}

Matrix

A = \begin{pmatrix}
  a_{11} & a_{12} & a_{13} \\
  a_{21} & a_{22} & a_{23} \\
  a_{31} & a_{32} & a_{33}
\end{pmatrix}

\begin{bmatrix}
  1 & 0 & 0 \\
  0 & 1 & 0 \\
  0 & 0 & 1
\end{bmatrix}

Aligned Equations

\begin{aligned}
  a &= b + c \\
  d &= e + f + g \\
  h &= i + j + k + l
\end{aligned}

Fractions and Binomials

\frac{n!}{k!(n-k)!} = \binom{n}{k}

Limits and Calculus

\lim_{x \to 0} \frac{\sin x}{x} = 1

\frac{d}{dx}\left( \int_{a}^{x} f(t)\,dt \right) = f(x)

Chemical Equations (mhchem)

\ce{H2O}

\ce{CO2 + H2O -> H2CO3}

\ce{2H2 + O2 ->[\text{combustion}] 2H2O}

\ce{Fe^{2+} + 2OH^{-} -> Fe(OH)2 v}

Trigonometric Functions

\sin^2\theta + \cos^2\theta = 1

e^{i\pi} + 1 = 0

Summation and Product

\prod_{i=1}^{n} x_i = x_1 \cdot x_2 \cdots x_n

\sum_{k=0}^{\infty} \frac{x^k}{k!} = e^x

Set Notation

A \cup B = \{x : x \in A \text{ or } x \in B\}

A \cap B = \{x : x \in A \text{ and } x \in B\}

\forall x \in \mathbb{R}, \exists y \in \mathbb{R} : x + y = 0