This is a test file for writing mathematical formulas in #NostrMarkup

This document demonstrates rendering formulas in TeX/LaTeX notation. It is intended for clients that render TeX with KaTeX/MathJax-style delimiters. If you want the entire document to be treated as math, put it in a dedicated math/code block. In general, it is better to keep prose as prose and only mark formulas as math. The general rule is:

• Inline math: $...$
• Display math: $$...$$ (on its own line)

TeX Examples

Inline equation: $E=mc^2$ Same equation in display mode: $$E=mc^2$$ Something more complex, inline: $\sqrt{x^2+1}$ and $\sqrt[3]{27}$ Something complex, in display mode: $$P \left( A=2 \,\middle|\, \dfrac{A^2}{B}>4 \right)$$ Another example: $$\prod_{i=1}^{n} x_i - 1$$ Function example:

$$
f(x)=
\begin{cases}
\frac{1}{d_{ij}} & \quad \text{when } d_{ij} \leq 160 \\
0 & \quad \text{otherwise}
\end{cases}
$$
And a matrix:

$$
M =
\begin{bmatrix}
\frac{5}{6} & \frac{1}{6} & 0 \\[0.3em]
\frac{5}{6} & 0 & \frac{1}{6} \\[0.3em]
0 & \frac{5}{6} & \frac{1}{6}
\end{bmatrix}
$$
Greek letters are a snap: $\Psi$, $\psi$, $\Phi$, $\phi$.

Equations within text are easy — a well-known Maxwell thermodynamic relation is $\left.\frac{\partial T}{\partial P}\right|_{s} = \left.\frac{\partial v}{\partial s}\right|_{P}$.

Using the quadratic formula, the roots of $x^2-6x+4=0$ are:

$$x = \frac{6 \pm \sqrt{36-16}}{2}$$

$$x = \frac{6 \pm \sqrt{20}}{2}$$

$$x \approx 0.8 \text{ or } 5.2$$

to 1 decimal place: $$x \approx 0.8 \text{ or } 5.2$$.

Advanced alignment and matrices:

A $3 \times 3$ matrix:

$$\begin{pmatrix}1&2&3\\4&5&6\\7&8&9\end{pmatrix}$$

and a $2 \times 1$ vector:

$$\begin{pmatrix}1\\0\end{pmatrix}$$

Determinant example:

$$\begin{vmatrix}a&b\\c&d\end{vmatrix}=ad-bc$$

A general $m \times n$ matrix:

$$\begin{pmatrix} a_{11} & \cdots & a_{1n}\\ \vdots & \ddots & \vdots\\ a_{m1} & \cdots & a_{mn} \end{pmatrix}$$

Mixed Examples
LaTeX inline: $\frac{1}{2}$
LaTeX display: $$\sum_{i=1}^n x_i$$
LaTeX matrix: $$\begin{pmatrix} a & b \\ c & d \end{pmatrix}$$
Edge Cases
Empty math: $$
Just delimiters: $ $
Dollar signs in text: The price is $10.50
Currency: $19.99
Shell command: echo "Price: $100"
JavaScript template: ``const price = `$${amount}```
CSS with dollar signs: color: $primary-color
This document demonstrates that LaTeX is processed correctly with standard math delimiters.