Math Rendering Test

Inline Math

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

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

Euler's identity: \(e^{i\pi} + 1 = 0\)

Gaussian integral:

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

Maxwell's equations (Gauss's law):

\[\nabla \cdot \mathbf{E} = \frac{\rho}{\varepsilon_0}\]

A matrix:

\[A = \begin{pmatrix} a & b \\ c & d \end{pmatrix}\]

Taylor series expansion:

\[f(x) = \sum_{n=0}^{\infty} \frac{f^{(n)}(a)}{n!}(x - a)^n\]

Given a probability distribution \(p(x)\), the entropy is defined as:

\[H(X) = -\sum_{x \in \mathcal{X}} p(x) \log p(x)\]

For continuous distributions, this becomes \(H(X) = -\int p(x) \log p(x)\, dx\).

Python:

def fibonacci(n: int) -> int:
    if n <= 1:
        return n
    return fibonacci(n - 1) + fibonacci(n - 2)

print(fibonacci(10))  # 55

JavaScript:

const greet = (name) => `Hello, ${name}!`;
console.log(greet("World"));

SPARQL:

SELECT ?subject ?predicate ?object
WHERE {
  ?subject ?predicate ?object .
  FILTER(?subject = <http://example.org/resource>)
}