Testing LaTeX & KaTeX: Benchmarking Formula Typography
A sandbox benchmark validating inline equations, algebraic radicals, and quantum state formulations rendered via client-side KaTeX.
A live benchmark and sandbox validating client-side KaTeX rendering across inline typography, algebraic equations, and complex physics notation.
1. Inline Fractions & Algebraic Radicals
Inline mathematics must integrate smoothly with body copy without pushing line heights or causing jarring vertical jitter.
- Simple rational fraction: $\frac{2}{4} = \frac{1}{2}$
- The quadratic discriminant: $\Delta = \sqrt{b^2 - 4ac}$
- Roots of a quadratic polynomial:
$$
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
$$
2. Fundamental Quantum Dynamics
The time-dependent Schrödinger equation governing the evolution of a quantum state vector $|\Psi(t)\rangle$ in Hilbert space:
$$
i\hbar \frac{\partial}{\partial t} |\Psi(t)\rangle = \hat{H} |\Psi(t)\rangle
$$
Where:
- $\hbar$ is the reduced Planck constant ($\frac{h}{2\pi}$)
- $\hat{H}$ is the Hamiltonian operator representing the total energy of the physical system
- $|\Psi(t)\rangle$ is the state ket vector
All equations scale sharply across dark and light modes with sub-millisecond execution.