The Hugo-Carbon Modular Engine includes high-performance mathematical typesetting powered by self-hosted KaTeX and the open-source IBM Plex Math typeface. It executes 100% locally in browser memory without external CDN requests.

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1. Mathematical Delimiters & Syntax

Mathematical formulas can be written using inline or display LaTeX syntax:

• Inline Formulas: Enclosed in $ ... $ or \( ... \)
• Display Block Formulas: Enclosed in $$ ... $$ or \[ ... \]

Inline Math Examples

• The pythagorean theorem is $a^2 + b^2 = c^2$.
• The Euler-Lagrange equation is $\frac{d}{dt} \left( \frac{\partial L}{\partial \dot{q}_i} \right) - \frac{\partial L}{\partial q_i} = 0$.
• Quantum wave function superposition: $|\psi\rangle = \alpha |0\rangle + \beta |1\rangle$.

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2. Advanced Mathematical Equations

Maxwell’s Equations of Electromagnetism

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}, \quad \nabla \cdot \mathbf{B} = 0$$$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}, \quad \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

Gaussian Integral & Normal Distribution

$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}$$$$f(x \mid \mu, \sigma^2) = \frac{1}{\sqrt{2\pi\sigma^2}} \exp\left( -\frac{(x - \mu)^2}{2\sigma^2} \right)$$

Linear Algebra: Eigenvalues & Matrices

$$\det(A - \lambda I) = 0$$

$$\begin{pmatrix} \cos\theta & -\sin\theta \ \sin\theta & \cos\theta \end{pmatrix} \begin{pmatrix} x \ y \end{pmatrix}

\begin{pmatrix} x\cos\theta - y\sin\theta \ x\sin\theta + y\cos\theta \end{pmatrix}$$

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3. Advanced Equation Card (math Shortcode)

For complex equations with title bars and copy buttons, the engine provides the math shortcode: