46 lines
1.4 KiB
Markdown
46 lines
1.4 KiB
Markdown
# Math Rendering Test
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## Inline Math
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The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ and Euler's identity is $e^{i\pi} + 1 = 0$.
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## Display Math
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$$\int_{-\infty}^{\infty} e^{-x^2} \, dx = \sqrt{\pi}$$
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$$\sum_{n=0}^{\infty} \frac{x^n}{n!} = e^x$$
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## Matrices
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$$\begin{pmatrix} a & b \\ c & d \end{pmatrix} \begin{pmatrix} x \\ y \end{pmatrix} = \begin{pmatrix} ax + by \\ cx + dy \end{pmatrix}$$
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## Aligned Equations
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$$\begin{aligned}
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\nabla \cdot \mathbf{E} &= \frac{\rho}{\varepsilon_0} \\
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\nabla \cdot \mathbf{B} &= 0 \\
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\nabla \times \mathbf{E} &= -\frac{\partial \mathbf{B}}{\partial t} \\
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\nabla \times \mathbf{B} &= \mu_0 \mathbf{J} + \mu_0 \varepsilon_0 \frac{\partial \mathbf{E}}{\partial t}
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\end{aligned}$$
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## Fractions and Nested Expressions
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$$\cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \cfrac{1}{1 + \cdots}}}}$$
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$$\binom{n}{k} = \frac{n!}{k!(n-k)!}$$
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## Limits and Calculus
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$$\lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n = e$$
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$$\oint_{\partial \Sigma} \mathbf{B} \cdot d\boldsymbol{\ell} = \mu_0 \iint_{\Sigma} \mathbf{J} \cdot d\mathbf{S} + \mu_0 \varepsilon_0 \frac{d}{dt} \iint_{\Sigma} \mathbf{E} \cdot d\mathbf{S}$$
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## Greek and Symbols
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$$\Gamma(z) = \int_0^{\infty} t^{z-1} e^{-t} \, dt, \quad \Re(z) > 0$$
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$$\mathcal{L}\{f(t)\} = \int_0^{\infty} f(t) e^{-st} \, dt$$
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## Cases
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$$|x| = \begin{cases} x & \text{if } x \geq 0 \\ -x & \text{if } x < 0 \end{cases}$$
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