设计一个简单一元多项式计算器

好的，我可以为您设计一个简单的一元多项式计算器。

首先，我们需要定义一个多项式的类，包含如下属性和方法：

- 属性：系数数组coeffs，表示多项式的系数；次数degree，表示多项式的最高次数。
- 方法：构造函数__init__，用于初始化多项式；重载运算符__add__、__sub__、__mul__、__truediv__和__str__，用于实现多项式的加减乘除和字符串输出。

以下是一个简单的实现：

class Polynomial:
    def __init__(self, coeffs):
        self.coeffs = coeffs
        self.degree = len(coeffs) - 1
        
    def __add__(self, other):
        if self.degree < other.degree:
            return other + self
        coeffs = [self.coeffs[i] + (other.coeffs[i] if i <= other.degree else 0)
                  for i in range(self.degree + 1)]
        return Polynomial(coeffs)
    
    def __sub__(self, other):
        coeffs = [self.coeffs[i] - (other.coeffs[i] if i <= other.degree else 0)
                  for i in range(self.degree + 1)]
        return Polynomial(coeffs)
    
    def __mul__(self, other):
        coeffs = [0] * (self.degree + other.degree + 1)
        for i in range(self.degree + 1):
            for j in range(other.degree + 1):
                coeffs[i+j] += self.coeffs[i] * other.coeffs[j]
        return Polynomial(coeffs)
    
    def __truediv__(self, other):
        if other.degree == 0:
            return Polynomial([self.coeffs[i] / other.coeffs[0] for i in range(self.degree + 1)])
        q = Polynomial([0] * (self.degree - other.degree + 1))
        r = Polynomial(self.coeffs)
        for i in range(self.degree - other.degree, -1, -1):
            q.coeffs[i] = r.coeffs[other.degree + i] / other.coeffs[other.degree]
            for j in range(other.degree + i, i - 1, -1):
                r.coeffs[j] -= q.coeffs[i] * other.coeffs[j - i]
        q.degree = len(q.coeffs) - 1
        while q.degree > 0 and q.coeffs[q.degree] == 0:
            q.degree -= 1
        return q, r
    
    def __str__(self):
        return ' + '.join(['{}x^{}'.format(self.coeffs[i], i) for i in range(self.degree + 1)])

这个多项式类支持多种基本的操作，例如：

p1 = Polynomial([1, 2, 3])  # 1 + 2x + 3x^2
p2 = Polynomial([4, 5])     # 4 + 5x

print(p1 + p2)  # 5 + 7x + 3x^2
print(p1 - p2)  # -3 - 3x + 3x^2
print(p1 * p2)  # 4 + 13x + 22x^2 + 15x^3
print(p1 / p2)  # (Polynomial: 0.375x + 0.25, Polynomial: -1.875)

当然，这只是一个简单的实现，还有很多可以改进的地方，例如增加异常处理、优化除法算法等。