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+/* eslint-disable no-irregular-whitespace */
+// Math Formulas Content
+export const MATH_FORMULAS_MD = String.raw`
+# Mathematical Formulas and Expressions
+
+This document demonstrates various mathematical notation and formulas that can be rendered using LaTeX syntax in markdown.
+
+## Basic Arithmetic
+
+### Addition and Summation
+$$\sum_{i=1}^{n} i = \frac{n(n+1)}{2}$$
+
+## Algebra
+
+### Quadratic Formula
+The solutions to $ax^2 + bx + c = 0$ are:
+$$x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$$
+
+### Binomial Theorem
+$$(x + y)^n = \sum_{k=0}^{n} \binom{n}{k} x^{n-k} y^k$$
+
+## Calculus
+
+### Derivatives
+The derivative of $f(x) = x^n$ is:
+$$f'(x) = nx^{n-1}$$
+
+### Integration
+$$\int_a^b f(x) \, dx = F(b) - F(a)$$
+
+### Fundamental Theorem of Calculus
+$$\frac{d}{dx} \int_a^x f(t) \, dt = f(x)$$
+
+## Linear Algebra
+
+### Matrix Multiplication
+If $A$ is an $m \times n$ matrix and $B$ is an $n \times p$ matrix, then:
+$$C_{ij} = \sum_{k=1}^{n} A_{ik} B_{kj}$$
+
+### Eigenvalues and Eigenvectors
+For a square matrix $A$, if $Av = \lambda v$ for some non-zero vector $v$, then:
+- $\lambda$ is an eigenvalue
+- $v$ is an eigenvector
+
+## Statistics and Probability
+
+### Normal Distribution
+The probability density function is:
+$$f(x) = \frac{1}{\sigma\sqrt{2\pi}} e^{-\frac{1}{2}\left(\frac{x-\mu}{\sigma}\right)^2}$$
+
+### Bayes' Theorem
+$$P(A|B) = \frac{P(B|A) \cdot P(A)}{P(B)}$$
+
+### Central Limit Theorem
+For large $n$, the sample mean $\bar{X}$ is approximately:
+$$\bar{X} \sim N\left(\mu, \frac{\sigma^2}{n}\right)$$
+
+## Trigonometry
+
+### Pythagorean Identity
+$$\sin^2\theta + \cos^2\theta = 1$$
+
+### Euler's Formula
+$$e^{i\theta} = \cos\theta + i\sin\theta$$
+
+### Taylor Series for Sine
+$$\sin x = \sum_{n=0}^{\infty} \frac{(-1)^n}{(2n+1)!} x^{2n+1} = x - \frac{x^3}{3!} + \frac{x^5}{5!} - \frac{x^7}{7!} + \cdots$$
+
+## Complex Analysis
+
+### Complex Numbers
+A complex number can be written as:
+$$z = a + bi = r e^{i\theta}$$
+
+where $r = |z| = \sqrt{a^2 + b^2}$ and $\theta = \arg(z)$
+
+### Cauchy-Riemann Equations
+For a function $f(z) = u(x,y) + iv(x,y)$ to be analytic:
+$$\frac{\partial u}{\partial x} = \frac{\partial v}{\partial y}, \quad \frac{\partial u}{\partial y} = -\frac{\partial v}{\partial x}$$
+
+## Differential Equations
+
+### First-order Linear ODE
+$$\frac{dy}{dx} + P(x)y = Q(x)$$
+
+Solution: $y = e^{-\int P(x)dx}\left[\int Q(x)e^{\int P(x)dx}dx + C\right]$
+
+### Heat Equation
+$$\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}$$
+
+## Number Theory
+
+### Prime Number Theorem
+$$\pi(x) \sim \frac{x}{\ln x}$$
+
+where $\pi(x)$ is the number of primes less than or equal to $x$.
+
+### Fermat's Last Theorem
+For $n > 2$, there are no positive integers $a$, $b$, and $c$ such that:
+$$a^n + b^n = c^n$$
+
+## Set Theory
+
+### De Morgan's Laws
+$$\overline{A \cup B} = \overline{A} \cap \overline{B}$$
+$$\overline{A \cap B} = \overline{A} \cup \overline{B}$$
+
+## Advanced Topics
+
+### Riemann Zeta Function
+$$\zeta(s) = \sum_{n=1}^{\infty} \frac{1}{n^s} = \prod_{p \text{ prime}} \frac{1}{1-p^{-s}}$$
+
+### Maxwell's Equations
+$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$
+$$\nabla \cdot \mathbf{B} = 0$$
+$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$
+$$\nabla \times \mathbf{B} = \mu_0\mathbf{J} + \mu_0\epsilon_0\frac{\partial \mathbf{E}}{\partial t}$$
+
+### Schrödinger Equation
+$$i\hbar\frac{\partial}{\partial t}\Psi(\mathbf{r},t) = \hat{H}\Psi(\mathbf{r},t)$$
+
+## Inline Math Examples
+
+Here are some inline mathematical expressions:
+
+- The golden ratio: $\phi = \frac{1 + \sqrt{5}}{2} \approx 1.618$
+- Euler's number: $e = \lim_{n \to \infty} \left(1 + \frac{1}{n}\right)^n$
+- Pi: $\pi = 4 \sum_{n=0}^{\infty} \frac{(-1)^n}{2n+1}$
+- Square root of 2: $\sqrt{2} = 1.41421356...$
+
+## Fractions and Radicals
+
+Complex fraction: $\frac{\frac{a}{b} + \frac{c}{d}}{\frac{e}{f} - \frac{g}{h}}$
+
+Nested radicals: $\sqrt{2 + \sqrt{3 + \sqrt{4 + \sqrt{5}}}}$
+
+## Summations and Products
+
+### Geometric Series
+$$\sum_{n=0}^{\infty} ar^n = \frac{a}{1-r} \quad \text{for } |r| < 1$$
+
+### Product Notation
+$$n! = \prod_{k=1}^{n} k$$
+
+### Double Summation
+$$\sum_{i=1}^{m} \sum_{j=1}^{n} a_{ij}$$
+
+## Limits
+
+$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
+
+$$\lim_{n \to \infty} \left(1 + \frac{x}{n}\right)^n = e^x$$
+
+## Further Bracket Styles and Amounts
+
+-  \( \mathrm{GL}_2(\mathbb{F}_7) \): Group of invertible matrices with entries in \(\mathbb{F}_7\).
+- Some kernel of \(\mathrm{SL}_2(\mathbb{F}_7)\):
+  \[
+  \left\{ \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}, \begin{pmatrix} -1 & 0 \\ 0 & -1 \end{pmatrix} \right\} = \{\pm I\}
+  \]
+- Algebra:
+\[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- $100 and $12.99 are amounts, not LaTeX.
+- I have $10, $3.99 and $x + y$ and $100x$. The amount is $2,000.
+- Emma buys 2 cupcakes for $3 each and 1 cookie for $1.50. How much money does she spend in total?
+- Maria has $20. She buys a notebook for $4.75 and a pack of pencils for $3.25. How much change does she receive?
+- 1 kg の質量は
+  \[
+  E = (1\ \text{kg}) \times (3.0 \times 10^8\ \text{m/s})^2 \approx 9.0 \times 10^{16}\ \text{J}
+  \]
+  というエネルギーに相当します。これは約 21 百万トンの TNT が爆発したときのエネルギーに匹敵します。
+- Algebra: \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\]
+- Algebraic topology, Homotopy Groups of $\mathbb{S}^3$:
+$$\pi_n(\mathbb{S}^3) = \begin{cases}
+\mathbb{Z} & n = 3 \\
+0 & n > 3, n \neq 4 \\
+\mathbb{Z}_2 & n = 4 \\
+\end{cases}$$
+- Spacer preceded by backslash:
+\[
+\boxed{
+\begin{aligned}
+N_{\text{att}}^{\text{(MHA)}} &=
+h \bigl[\, d_{\text{model}}\;d_{k} + d_{\text{model}}\;d_{v}\, \bigr]   && (\text{Q,K,V の重み})\\
+&\quad+ h(d_{k}+d_{k}+d_{v})                                          && (\text{バイアス Q,K,V）}\\[4pt]
+&\quad+ (h d_{v})\, d_{\text{model}}                                 && (\text{出力射影 }W^{O})\\
+&\quad+ d_{\text{model}}                                            && (\text{バイアス }b^{O})
+\end{aligned}}
+\]
+
+## Formulas in a Table
+
+| Area | Expression | Comment |
+|------|------------|---------|
+| **Algebra** | \[
+x = \frac{-b \pm \sqrt{\,b^{2}-4ac\,}}{2a}
+\] | Quadratic formula |
+| | \[
+(a+b)^{n} = \sum_{k=0}^{n}\binom{n}{k}\,a^{\,n-k}\,b^{\,k}
+\] | Binomial theorem |
+| | \(\displaystyle \prod_{k=1}^{n}k = n! \) | Factorial definition |
+| **Geometry** | \( \mathbf{a}\cdot \mathbf{b} = \|\mathbf{a}\|\,\|\mathbf{b}\|\,\cos\theta \) | Dot product & angle |
+
+## No math (but chemical)
+
+Balanced chemical reaction with states:
+
+\[
+\ce{2H2(g) + O2(g) -> 2H2O(l)}
+\]
+
+The standard enthalpy change for the reaction is: $\Delta H^\circ = \pu{-572 kJ mol^{-1}}$.
+
+---
+
+*This document showcases various mathematical notation and formulas that can be rendered in markdown using LaTeX syntax.*
+`;