模組:PythonScript/Examples/MyPyMath.py

import math

# 1. 費氏數列計算 (O(log n) 快速倍增法)
# 效能極高且遞迴深度極淺 (計算 n=100 僅需約 7 層遞迴)，完美避開 Stack Overflow 限制
def _fib_fast_doubling(n):
    if n == 0:
        return (0, 1)
    else:
        a, b = _fib_fast_doubling(n // 2)
        c = a * (b * 2 - a)
        d = a * a + b * b
        if n % 2 == 0:
            return (c, d)
        else:
            return (d, c + d)

def calc_fibonacci(n):
    """計算第 n 個費氏數"""
    if not isinstance(n, int):
        raise TypeError("n must be an integer")
    if n < 0:
        raise ValueError("n must be non-negative")
    
    return _fib_fast_doubling(n)[0]


# 2. 具備實際運算功能的 2D 向量類別
class MyVector:
    def __init__(self, x, y):
        self.x = x
        self.y = y
        
    def norm(self):
        """計算向量長度 (L2 Norm / 歐幾里得距離)"""
        return math.hypot(self.x, self.y)
        
    def __add__(self, other):
        """支援向量相加 (v1 + v2)"""
        if isinstance(other, MyVector):
            return MyVector(self.x + other.x, self.y + other.y)
        return NotImplemented
        
    def __mul__(self, scalar):
        """支援向量與純量相乘 (v * 3)"""
        if isinstance(scalar, (int, float)):
            return MyVector(self.x * scalar, self.y * scalar)
        return NotImplemented
        
    def __rmul__(self, scalar):
        """支援純量與向量相乘 (3 * v)"""
        return self.__mul__(scalar)
        
    def __repr__(self):
        """優化 print 輸出格式"""
        return f"MyVector(x={self.x}, y={self.y})"

if __name__ == "__main__":
    # 可直接像呼叫原生 Lua 函式一樣呼叫 Python 函式或實例化 Python 類別！
    print(f"fib(100)={calc_fibonacci(100)}")
    obj = MyVector(3, 4)
    print(obj.norm())