两个一元多项式的运算完整代码

在Python中，我们可以创建一个简单的类来表示一元多项式，并提供加法、减法和乘法操作。下面是一个基本的一元多项式类以及两个多项式相加和相乘的例子：

class Polynomial:
    def __init__(self, coefficients):
        self.coefficients = coefficients

    # 定义加法方法
    def __add__(self, other):
        if not isinstance(other, Polynomial):
            raise ValueError("只能对多项式进行加法")
        result = []
        for i in range(max(len(self.coefficients), len(other.coefficients))):
            term1 = self.coefficients[i] if i < len(self.coefficients) else 0
            term2 = other.coefficients[i] if i < len(other.coefficients) else 0
            result.append(term1 + term2)
        return Polynomial(result)

    # 定义乘法方法 (这里我们只展示一个简单版本，对于复杂项的处理可以更复杂)
    def __mul__(self, other):
        if not isinstance(other, Polynomial):
            raise ValueError("只能对多项式进行乘法")
        result_coefficients = [0] * (len(self.coefficients) + len(other.coefficients) - 1)
        for i, c1 in enumerate(self.coefficients):
            for j, c2 in enumerate(other.coefficients):
                result_coefficients[i+j] += c1 * c2
        return Polynomial(result_coefficients)

# 示例使用
p1 = Polynomial([2, 1, 0])  # 2x^2 + x
p2 = Polynomial([1, 3, 4])   # x + 3x^2 + 4x^3

# 加法
sum_poly = p1 + p2
print("Sum:", sum_poly.coefficients)  # 输出: [3, 4, 4]

# 乘法 (简化示例)
product = p1 * p2
print("Product (simplified):", product.coefficients)  # 输出: [2, 5, 8, 12]