设有一元多项式Am(x)和Bn(X)，编程实现多项式Am(x)和Bn(x)的加法、减法和乘法运算。其中多项式描述为： Am(x)=A0+A1x1+A2x2+A3x3+….+Amxm； Bn(x)=B0+B1x1+B2x2+B3x3+….+Bnxn。

以下是Python代码实现多项式的加法、减法和乘法运算：

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

    def __add__(self, other):
        new_coefficients = []
        for i in range(max(len(self.coefficients), len(other.coefficients))):
            if i < len(self.coefficients) and i < len(other.coefficients):
                new_coefficients.append(self.coefficients[i] + other.coefficients[i])
            elif i < len(self.coefficients):
                new_coefficients.append(self.coefficients[i])
            else:
                new_coefficients.append(other.coefficients[i])
        return Polynomial(new_coefficients)

    def __sub__(self, other):
        new_coefficients = []
        for i in range(max(len(self.coefficients), len(other.coefficients))):
            if i < len(self.coefficients) and i < len(other.coefficients):
                new_coefficients.append(self.coefficients[i] - other.coefficients[i])
            elif i < len(self.coefficients):
                new_coefficients.append(self.coefficients[i])
            else:
                new_coefficients.append(-other.coefficients[i])
        return Polynomial(new_coefficients)

    def __mul__(self, other):
        new_coefficients = [0] * (len(self.coefficients) + len(other.coefficients) - 1)
        for i in range(len(self.coefficients)):
            for j in range(len(other.coefficients)):
                new_coefficients[i+j] += self.coefficients[i] * other.coefficients[j]
        return Polynomial(new_coefficients)

    def __str__(self):
        result = ""
        for i, coefficient in enumerate(self.coefficients):
            if coefficient != 0:
                if i == 0:
                    result += str(coefficient)
                elif i == 1:
                    result += f"{'+' if coefficient > 0 else ''}{coefficient}x"
                else:
                    result += f"{'+' if coefficient > 0 else ''}{coefficient}x^{i}"
        if result == "":
            result = "0"
        return result

其中，`__add__` 方法实现了多项式的加法运算，`__sub__` 方法实现了多项式的减法运算，`__mul__` 方法实现了多项式的乘法运算。`__str__` 方法用于将多项式对象转换为字符串。

使用示例：

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

C = A + B                   # 加法运算，C(x) = 5 + 7x + 3x^2
print(C)

D = A - B                   # 减法运算，D(x) = -3 - 3x + 3x^2
print(D)

E = A * B                   # 乘法运算，E(x) = 4 + 13x + 22x^2 + 15x^3
print(E)