YYiki: Examples

2025-08-28 → 2025-12-11

Mathematics and Code Examples

This page demonstrates the rich content support in YYiki Static, including mathematical notation and syntax-highlighted code.

Mathematical Expressions

YYiki Static supports KaTeX for beautiful math rendering.

Inline Math

The quadratic formula is $x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}$ where $a \neq 0$.

Display Math

The Gaussian integral:

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

Euler’s identity:

$$e^{i\pi} + 1 = 0$$

Complex Equations

Maxwell’s equations in differential form:

$$\nabla \cdot \mathbf{E} = \frac{\rho}{\epsilon_0}$$

$$\nabla \cdot \mathbf{B} = 0$$

$$\nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t}$$

$$\nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t}$$

Code Examples

Python

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

    fib_sequence = [0, 1]
    for i in range(2, n):
        fib_sequence.append(fib_sequence[-1] + fib_sequence[-2])

    return fib_sequence

# Example usage
print(fibonacci(10))
# Output: [0, 1, 1, 2, 3, 5, 8, 13, 21, 34]

JavaScript

// Async function to fetch data from an API
async function fetchUserData(userId) {
    try {
        const response = await fetch(`/api/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 with async/await
(async () => {
    const user = await fetchUserData(123);
    console.log(user);
})();

Bash

#!/bin/bash

# Function to check if a command exists
command_exists() {
    command -v "$1" >/dev/null 2>&1
}

# Check for required tools
for tool in git python3 uv; do
    if command_exists "$tool"; then
        echo "✓ $tool is installed"
    else
        echo "✗ $tool is not installed"
        exit 1
    fi
done

echo "All required tools are installed!"

SQL

-- Create a view for active users with their latest posts
CREATE VIEW active_users_latest_posts AS
SELECT 
    u.id,
    u.username,
    u.email,
    p.title AS latest_post_title,
    p.created_at AS latest_post_date
FROM users u
LEFT JOIN LATERAL (
    SELECT title, created_at
    FROM posts
    WHERE user_id = u.id
      AND status = 'published'
    ORDER BY created_at DESC
    LIMIT 1
) p ON true
WHERE u.active = true
  AND u.last_login > NOW() - INTERVAL '30 days';

Combining Math and Code

Here’s an example implementing the quadratic formula in Python:

import math

def solve_quadratic(a, b, c):
    """
    Solve quadratic equation ax² + bx + c = 0
    Returns tuple of solutions or None if no real solutions
    """
    if a == 0:
        raise ValueError("'a' cannot be zero for a quadratic equation")

    discriminant = b**2 - 4*a*c

    if discriminant < 0:
        return None  # No real solutions
    elif discriminant == 0:
        x = -b / (2*a)
        return (x, x)  # One solution (repeated root)
    else:
        sqrt_discriminant = math.sqrt(discriminant)
        x1 = (-b + sqrt_discriminant) / (2*a)
        x2 = (-b - sqrt_discriminant) / (2*a)
        return (x1, x2)

# Example: solve x² - 5x + 6 = 0
solutions = solve_quadratic(1, -5, 6)
print(f"Solutions: {solutions}")  # Output: Solutions: (3.0, 2.0)

The discriminant $\Delta = b^2 - 4ac$ determines the nature of the roots: - If $\Delta > 0$: Two distinct real roots - If $\Delta = 0$: One repeated real root - If $\Delta < 0$: No real roots (complex conjugate pairs)

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