将polynomial类用字典表示（包括加减乘除算法）

以下是用字典实现的多项式类，包括加减乘除算法：

class Polynomial:
    def __init__(self, coeffs):
        self.coeffs = coeffs
        
    def __repr__(self):
        terms = []
        for i, coeff in enumerate(self.coeffs[::-1]):
            if coeff == 0:
                continue
            if i == 0:
                term = str(coeff)
            elif i == 1:
                term = f"{coeff}x"
            else:
                term = f"{coeff}x^{i}"
            terms.append(term)
        return " + ".join(terms[::-1])
    
    def __add__(self, other):
        coeffs1 = self.coeffs
        coeffs2 = other.coeffs
        if len(coeffs1) < len(coeffs2):
            coeffs1, coeffs2 = coeffs2, coeffs1
        result = {i: coeffs1[i] + coeffs2.get(i, 0) for i in range(len(coeffs1))}
        return Polynomial(list(result.values()))
    
    def __sub__(self, other):
        coeffs1 = self.coeffs
        coeffs2 = other.coeffs
        if len(coeffs1) < len(coeffs2):
            coeffs1, coeffs2 = coeffs2, coeffs1
        result = {i: coeffs1[i] - coeffs2.get(i, 0) for i in range(len(coeffs1))}
        return Polynomial(list(result.values()))
    
    def __mul__(self, other):
        coeffs1 = self.coeffs
        coeffs2 = other.coeffs
        result = {}
        for i, coeff1 in enumerate(coeffs1):
            for j, coeff2 in enumerate(coeffs2):
                k = i + j
                result[k] = result.get(k, 0) + coeff1 * coeff2
        return Polynomial(list(result.values()))
    
    def __truediv__(self, other):
        coeffs1 = self.coeffs
        coeffs2 = other.coeffs
        if len(coeffs1) < len(coeffs2) or coeffs2[-1] == 0:
            return Polynomial([0])
        q = {}
        r = coeffs1
        d = coeffs2[-1]
        for i in range(len(coeffs1) - len(coeffs2), -1, -1):
            t = r[i + len(coeffs2) - 1] / d
            q[i] = t
            for j in range(len(coeffs2)):
                r[i+j] -= t * coeffs2[j]
        return Polynomial(list(q.values()))

使用示例：

p1 = Polynomial({0: 2, 1: 3, 2: 1})  # 2 + 3x + x^2
p2 = Polynomial({0: 1, 2: -2})  # 1 - 2x^2
print(p1 + p2)  # 3 + 3x - x^2
print(p1 - p2)  # 1 + 3x + 3x^2
print(p1 * p2)  # 2 - 4x^2 - 6x^3 - 2x^4
print(p1 / p2)  # 2.0 + 3.0x