test: add KaTex and MathJax test files for rendering examples

apps/test/content/posts/katex-test.md

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+---
+title: KaTex Test
+date: 2025-09-15T21:05:17+08:00
+collections:
+  - Tests
+categories:
+  - Markdown
+tags:
+  - Math
+---
+
+Testing KaTex rendering in FixIt theme.
+
+<!--more-->
+
+## Inline Formulas
+
+$c = \pm\sqrt{a^2 + b^2}$ and \(f(x)=\int_{-\infty}^{\infty} \hat{f}(\xi) e^{2 \pi i \xi x} d \xi\)
+
+## Formula Blocks
+
+$$ c = \pm\sqrt{a^2 + b^2} $$
+
+\[f(x)=\int_{-\infty}^{\infty} \hat{f}(\xi) e^{2 \pi i \xi x} d \xi\]
+
+$$
+\begin{equation*}
+  \rho \frac{\mathrm{D} \mathbf{v}}{\mathrm{D} t}=\nabla \cdot \mathbb{P}+\rho \mathbf{f}
+\end{equation*}
+$$
+
+$$
+\begin{equation}
+  \mathbf{E}=\sum_{i} \mathbf{E}\_{i}=\mathbf{E}\_{1}+\mathbf{E}\_{2}+\mathbf{E}_{3}+\cdots
+\end{equation}
+$$
+
+$$
+\begin{align}
+  a&=b+c \\
+  d+e&=f
+\end{align}
+$$
+
+$$
+\begin{alignat}{2}
+   10&x+&3&y = 2 \\
+   3&x+&13&y = 4
+\end{alignat}
+$$
+
+$$
+\begin{gather}
+   a=b \\
+   e=b+c
+\end{gather}
+$$
+
+$$
+\begin{CD}
+   A @>a>> B \\
+@VbVV @AAcA \\
+   C @= D
+\end{CD}
+$$
+
+## Chemical Equations
+
+$$ \ce{CO2 + C -> 2 CO} $$
+
+$$ \ce{Hg^2+ ->[I-] HgI2 ->[I-] [Hg^{II}I4]^2-} $$
+
+$$C_p[\ce{H2O(l)}] = \pu{75.3 J // mol K}$$

apps/test/content/posts/mathjax-test.md

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