Testing code and latex with markdown

This post demonstrates full LaTeX rendering and code syntax highlighting in MDX.

Inline Mathematics

Einstein's famous equation $E = mc^2$ relates energy to mass. The quadratic formula $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ solves any quadratic equation.

Block Mathematics

The Gaussian integral is one of the most beautiful results in mathematics:

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

The Euler Identity

Perhaps the most elegant equation in all of mathematics:

e^{i\pi} + 1 = 0

This single equation connects five fundamental constants: $e$ , $i$ , $\pi$ , $1$ , and $0$ .

Fourier Transform

The Fourier transform decomposes a function into its constituent frequencies:

\hat{f}(\xi) = \int_{-\infty}^{\infty} f(x) e^{-2\pi i x \xi} \, dx

Maxwell's Equations

The four Maxwell equations in differential form:

\begin{aligned} \nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_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 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t} \end{aligned}

Matrices and Linear Algebra

A rotation matrix in 2D:

R(\theta) = \begin{pmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{pmatrix}

Summations and Products

The Basel problem:

\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}

Euler's product formula for the Riemann zeta function:

\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \prod_{p \text{ prime}} \frac{1}{1 - p^{-s}}

Code Example

Here's how you might compute the Gaussian integral numerically in Python:

import numpy as np
from scipy import integrate
 
def gaussian(x):
    return np.exp(-x**2)
 
result, error = integrate.quad(gaussian, -np.inf, np.inf)
print(f"Result: {result:.10f}")  # Should be close to sqrt(pi) ≈ 1.7724538509

Conclusion

LaTeX rendering in MDX enables writing rich mathematical content with beautiful typography, perfect for technical blogs, documentation, and educational materials.