# Comprehensive Test Document
This document combines unicode, math, and code to test all new capabilities.
## Section 1: Multilingual Content
### English
Hello World! This is a test of PDF generation with unicode support.
### 中文 (Chinese)
你好世界！这是PDF生成的测试。数学公式：$E = mc^2$
### 日本語 (Japanese)
こんにちは世界！数式：$\pi \approx 3.14159$
### 한국어 (Korean)
안녕하세요！수학: $a^2 + b^2 = c^2$
## Section 2: Mathematical Content
The area of a circle with radius $r$ is given by:
$$
A = \pi r^2
$$
The volume of a sphere is:
$$
V = \frac{4}{3}\pi r^3
$$
### Statistical Formulas
Mean: $\mu = \frac{1}{n}\sum_{i=1}^{n} x_i$
Standard deviation:
$$
\sigma = \sqrt{\frac{1}{n}\sum_{i=1}^{n}(x_i - \mu)^2}
$$
## Section 3: Code Examples
### Python with Unicode Comments
```python
# 计算斐波那契数列 (Calculate Fibonacci sequence)
def fibonacci(n):
"""
Calcule la séquence de Fibonacci
Вычисляет последовательность Фибоначчи
"""
if n <= 1:
return n
return fibonacci(n-1) + fibonacci(n-2)
# Test: 测试
print(f"Fibonacci(10) = {fibonacci(10)}")
```
### Rust with Math in Comments
```rust
// Calculate π using Leibniz formula: π = 4∑((-1)^n)/(2n+1)
fn calculate_pi(iterations: u32) -> f64 {
let mut pi = 0.0;
for n in 0..iterations {
let sign = if n % 2 == 0 { 1.0 } else { -1.0 };
pi += sign / (2.0 * n as f64 + 1.0);
}
4.0 * pi
}
```
## Section 4: Mixed Content Table
| English | Hello | ∑ (sum) |
| 中文 | 你好 | ∫ (integral)|
| 日本語 | こんにちは | ∞ (infinity)|
| 한국어 | 안녕하세요 | ≈ (approx) |
| Русский | Привет | ∀ (forall) |
## Section 5: Special Characters and Symbols
### Currency
$ € £ ¥ ₹ ₽ ₩ ₿
### Math Symbols
∀ ∃ ∈ ∉ ∑ ∏ ∫ ∂ ∇ √ ∞ ≠ ≈ ≤ ≥ ± × ÷
### Arrows
← → ↑ ↓ ↔ ⇐ ⇒ ⇔
### Greek Letters
α β γ δ ε ζ η θ ι κ λ μ ν ξ ο π ρ σ τ υ φ χ ψ ω
## Section 6: Complex Math with Code
The Fast Fourier Transform (FFT) algorithm:
$$
X_k = \sum_{n=0}^{N-1} x_n \cdot e^{-i2\pi kn/N}
$$
Implementation:
```python
import numpy as np
def fft(x):
"""
Compute FFT using Cooley-Tukey algorithm
Time complexity: O(N log N)
"""
N = len(x)
if N <= 1:
return x
even = fft(x[0::2])
odd = fft(x[1::2])
T = [np.exp(-2j * np.pi * k / N) * odd[k] for k in range(N // 2)]
return [even[k] + T[k] for k in range(N // 2)] + \
[even[k] - T[k] for k in range(N // 2)]
```
## Section 7: Unicode in Code Blocks
```javascript
// Unicode variable names (valid in modern JS)
const π = Math.PI;
const 圆周率 = π;
const радиус = 5;
// Calculate area: A = πr²
const площадь = π * радиус ** 2;
console.log(`Area (面积): ${площадь}`);
```
## Section 8: Escape Sequences Test
Special characters that need escaping:
- Backslash: \\
- Parentheses: \( \)
- Brackets: \[ \]
- Braces: \{ \}
Octal sequences: \101 = A, \102 = B, \103 = C
## Conclusion
This document tests:
✓ Unicode characters from multiple scripts
✓ Mathematical expressions (inline and block)
✓ Code blocks with syntax highlighting
✓ Special symbols and characters
✓ Mixed content in tables
✓ Escape sequences