H1: Main Heading Test

This is a test post to showcase all the markdown and special features supported on this site. Let’s explore each capability systematically.

H2: Mathematical Equations with LaTeX

Inline math works great: $E = mc^2$ is Einstein’s famous equation. Here’s the quadratic formula: $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$.

Block equations are even more impressive:

$$\int_{-\infty}^{\infty} e^{-x^2} dx = \sqrt{\pi}$$

Here’s a more complex example showing the Fourier Transform:

$$F(\omega) = \int_{-\infty}^{\infty} f(t) e^{-i\omega t} dt$$

H3: Matrix Notation

Matrices work beautifully with KaTeX:

$$\begin{bmatrix} a & b \\ c & d \end{bmatrix} \begin{bmatrix} x \\ y \end{bmatrix} = \begin{bmatrix} ax + by \\ cx + dy \end{bmatrix}$$

H4: Summation and Products

Greek letters and operators are fully supported:

$$\sum_{n=1}^{\infty} \frac{1}{n^2} = \frac{\pi^2}{6}$$ $$\prod_{i=1}^{n} i = n!$$

H2: Code Highlighting

Let’s test syntax highlighting across multiple languages.

H3: Python Example

def fibonacci(n):
    """Generate Fibonacci sequence up to n terms."""
    if n <= 0:
        return []
    elif n == 1:
        return [0]
    
    sequence = [0, 1]
    while len(sequence) < n:
        sequence.append(sequence[-1] + sequence[-2])
    
    return sequence

# Calculate and print first 10 Fibonacci numbers
result = fibonacci(10)
print(f"First 10 Fibonacci numbers: {result}")

H3: JavaScript Example

// Modern JavaScript with async/await
async function fetchUserData(userId) {
  try {
    const response = await fetch(`https://api.example.com/users/${userId}`);
    
    if (!response.ok) {
      throw new Error(`HTTP error! status: ${response.status}`);
    }
    
    const data = await response.json();
    return data;
  } catch (error) {
    console.error('Failed to fetch user data:', error);
    return null;
  }
}

// Usage
const user = await fetchUserData(123);
console.log(user);

H3: TypeScript Example

interface User {
  id: number;
  name: string;
  email: string;
  role: 'admin' | 'user' | 'guest';
}

class UserManager {
  private users: Map<number, User> = new Map();
  
  addUser(user: User): void {
    this.users.set(user.id, user);
  }
  
  getUser(id: number): User | undefined {
    return this.users.get(id);
  }
  
  getAllAdmins(): User[] {
    return Array.from(this.users.values())
      .filter(user => user.role === 'admin');
  }
}

H3: Rust Example

use std::collections::HashMap;

fn word_frequency(text: &str) -> HashMap<String, usize> {
    let mut freq_map = HashMap::new();
    
    for word in text.split_whitespace() {
        let word = word.to_lowercase();
        *freq_map.entry(word).or_insert(0) += 1;
    }
    
    freq_map
}

fn main() {
    let text = "hello world hello rust world";
    let frequencies = word_frequency(text);
    
    for (word, count) in frequencies.iter() {
        println!("{}: {}", word, count);
    }
}

H2: Mermaid Diagrams

Mermaid allows us to create beautiful diagrams from text descriptions.

H3: Flowchart Example

graph TD
    A[Start] --> B{Is it working?}
    B -->|Yes| C[Great!]
    B -->|No| D[Debug]
    D --> E[Fix the bug]
    E --> B
    C --> F[Deploy]
    F --> G[End]

H3: Sequence Diagram

sequenceDiagram
    participant User
    participant Browser
    participant Server
    participant Database
    
    User->>Browser: Enter URL
    Browser->>Server: HTTP Request
    Server->>Database: Query data
    Database-->>Server: Return results
    Server-->>Browser: HTTP Response
    Browser-->>User: Display page

H3: Class Diagram

classDiagram
    class Animal {
        +String name
        +int age
        +makeSound()
        +eat()
    }
    
    class Dog {
        +String breed
        +bark()
        +fetch()
    }
    
    class Cat {
        +String color
        +meow()
        +purr()
    }
    
    Animal <|-- Dog
    Animal <|-- Cat

H3: State Diagram

stateDiagram-v2
    [*] --> Idle
    Idle --> Processing: Start Task
    Processing --> Success: Task Completed
    Processing --> Failed: Error Occurred
    Success --> Idle: Reset
    Failed --> Idle: Retry
    Failed --> [*]: Give Up

H2: Text Formatting

Let’s verify standard markdown formatting works properly:

• Bold text for emphasis
• Italic text for subtle emphasis
• Inline code for technical terms
• Strikethrough for corrections

H3: Lists

Unordered lists:

• First item
• Second item
  • Nested item 1
  • Nested item 2
• Third item

Ordered lists:

1. First step
2. Second step
   1. Sub-step A
   2. Sub-step B
3. Third step

H3: Blockquotes

This is a blockquote. It’s useful for highlighting important passages or quotes from other sources.

Multiple paragraphs in a blockquote work too!

H3: Horizontal Rules

Use horizontal rules to separate sections:

---

H2: Conclusion

This test post demonstrates that all core features are working correctly:

• ✅ Headings from H1 to H4
• ✅ LaTeX equations (inline and block)
• ✅ Syntax highlighting for multiple languages
• ✅ Mermaid diagrams (flowchart, sequence, class, state)
• ✅ Standard markdown formatting
• ✅ Lists and blockquotes

Everything looks great!