Math Rendering Test

This page tests LaTeX math rendering with MathJax.

Inline Math

Here's Einstein's famous equation: \(E = mc^2\)

The quadratic formula: \(x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\)

Greek letters: \(\alpha, \beta, \gamma, \Delta, \Sigma, \Omega\)

Display Math

Basic Equation

\[ f(x) = \int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi} \]

Matrix Example

\[ \begin{bmatrix} a_{11} & a_{12} & a_{13} \\ a_{21} & a_{22} & a_{23} \\ a_{31} & a_{32} & a_{33} \end{bmatrix} \]

Multi-line Alignment

\[ \begin{align} \nabla \cdot \mathbf{E} &= \frac{\rho}{\epsilon_0} \\ \nabla \cdot \mathbf{B} &= 0 \\ \nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\ \nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{align} \]

SpliceAI Example

The SpliceAI loss function:

\[ \mathcal{L} = -\sum_{i=1}^{L} \sum_{c \in \{A, D, N\}} y_{i,c} \log(\hat{y}_{i,c}) \]

where: - \(L\) is the sequence length - \(c\) represents splice site categories (Acceptor, Donor, Neither) - \(y_{i,c}\) is the true label - \(\hat{y}_{i,c}\) is the predicted probability

Probability Distribution

\[ P(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{(x-\mu)^2}{2\sigma^2}} \]

Advanced Examples

Summation and Product

\[ \sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6} \quad \text{and} \quad \prod_{p \text{ prime}} \frac{1}{1-p^{-s}} = \zeta(s) \]

Conditional Expression

\[ f(n) = \begin{cases} n/2 & \text{if } n \text{ is even} \\ 3n+1 & \text{if } n \text{ is odd} \end{cases} \]

Fraction and Binomial

\[ \binom{n}{k} = \frac{n!}{k!(n-k)!} \quad \text{for } 0 \leq k \leq n \]

---

If all equations above render properly (as typeset math, not raw LaTeX), then MathJax is working correctly! 🎉