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Cell
120 lines
2.3 KiB
Markdown
120 lines
2.3 KiB
Markdown
---
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title: MathJax Test
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date: 2025-09-15T21:05:17+08:00
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collections:
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- Tests
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categories:
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- Markdown
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tags:
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- Math
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math:
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type: mathjax
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mathjax:
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macros:
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bold: ["{\\bf #1}", 1] # usage: $\bold{math}$
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loader:
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load: ["ui/safe", "[tex]/physics", "[custom]/xypic.js"]
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paths:
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custom: "https://cdn.jsdelivr.net/gh/sonoisa/XyJax-v3@3.0.1/build/"
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packages:
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"[+]": ["physics", "xypic"]
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tex:
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physics:
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italicdiff: false
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arrowdel: false
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---
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Testing $\text{MathJax}$ rendering in FixIt theme.
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<!--more-->
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## Inline Formulas
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$c = \pm\sqrt{a^2 + b^2}$ and \(f(x)=\int_{-\infty}^{\infty} \hat{f}(\xi) e^{2 \pi i \xi x} d \xi\)
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## Formula Blocks
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$$ x = {-b \pm \sqrt{b^2-4ac} \over 2a} $$
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\[ f(a) = \frac{1}{2\pi i} \oint\frac{f(z)}{z-a}dz \]
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$$
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\cos(\theta+\phi)=\cos(\theta)\cos(\phi)−\sin(\theta)\sin(\phi)
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$$
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\[
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\int_D ({\nabla\cdot} F)dV=\int_{\partial D} F\cdot ndS
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\]
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$$
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\vec{\nabla} \times \vec{F} =
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\left( \frac{\partial F_z}{\partial y} - \frac{\partial F_y}{\partial z} \right) \mathbf{i}
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+ \left( \frac{\partial F_x}{\partial z} - \frac{\partial F_z}{\partial x} \right) \mathbf{j}
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+ \left( \frac{\partial F_y}{\partial x} - \frac{\partial F_x}{\partial y} \right) \mathbf{k}
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$$
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$$
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\sigma = \sqrt{ \frac{1}{N} \sum_{i=1}^N (x_i -\mu)^2}
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$$
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$$
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(\nabla_X Y)^k = X^i (\nabla_i Y)^k =
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X^i \left( \frac{\partial Y^k}{\partial x^i} + \Gamma_{im}^k Y^m \right)
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$$
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## Chemical Equations
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$$C_p[\ce{H2O(l)}] = \pu{75.3 J // mol K}$$
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$$ \ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-} $$
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$$C_p[\ce{H2O(l)}] = \pu{75.3 J // mol K}$$
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## Custom Macros
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$\bold{Custom}$ macro $\KaTeX$ in $\text{MathJax}$
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$$
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\def\RR{{\bf R}}
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\def\bolda#1{{\bf #1}}
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\RR = \bolda{R}
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$$
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$$
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\newcommand{\water}{{\rm H_{2}O}}
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\water = \text{H}_2\text{O}
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$$
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$$
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\newcommand{\hello}[1][World]{Hello, #1!}
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\hello \quad \hello[FixIt]
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$$
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$$
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\let\oldphi=\phi
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\let\oldtheta=\theta
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\renewcommand{\phi}{\varphi}
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\renewcommand{\theta}{\vartheta}
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\phi, \oldphi, \theta, \oldtheta
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$$
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## Custom Extensions
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A `physics` package example:
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$$
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\mqty(a & b \\ c & d) = \begin{pmatrix} a & b \\ c & d \end{pmatrix}
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$$
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An `xypic` package example:
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$$
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\begin{xy}
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\xymatrix {
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U \ar@/_/[ddr]_y \ar@{.>}[dr]|{\langle x,y \rangle} \ar@/^/[drr]^x \\
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& X \times_Z Y \ar[d]^q \ar[r]_p & X \ar[d]_f \\
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& Y \ar[r]^g & Z
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}
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\end{xy}
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$$
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