定义一个向量类，判断向量是否相等，并求模，加减乘除和向量积与数量积。用python

以下是一个基本的向量类的实现，包括判断向量相等、向量模、向量加减、向量乘除、向量积和数量积等操作：

class Vector:
    def __init__(self, lst):
        self._values = list(lst)

    def __repr__(self):
        return "Vector({})".format(self._values)

    def __str__(self):
        return "({})".format(", ".join(str(e) for e in self._values))

    def __len__(self):
        return len(self._values)

    def __getitem__(self, index):
        return self._values[index]

    def __setitem__(self, index, value):
        self._values[index] = value

    def __eq__(self, other):
        if len(self) != len(other):
            return False
        for i in range(len(self)):
            if self[i] != other[i]:
                return False
        return True

    def __add__(self, other):
        if len(self) != len(other):
            raise ValueError("Vectors must be of the same length")
        return Vector([self[i] + other[i] for i in range(len(self))])

    def __sub__(self, other):
        if len(self) != len(other):
            raise ValueError("Vectors must be of the same length")
        return Vector([self[i] - other[i] for i in range(len(self))])

    def __mul__(self, other):
        if isinstance(other, (int, float)):
            return Vector([self[i] * other for i in range(len(self))])
        elif isinstance(other, Vector):
            if len(self) != len(other):
                raise ValueError("Vectors must be of the same length")
            return sum([self[i] * other[i] for i in range(len(self))])
        else:
            raise TypeError("Multiplication is only defined for scalar and vector values")

    def __rmul__(self, other):
        return self.__mul__(other)

    def __truediv__(self, other):
        if isinstance(other, (int, float)):
            return Vector([self[i] / other for i in range(len(self))])
        else:
            raise TypeError("Division is only defined for scalar values")

    def cross(self, other):
        if len(self) != 3 or len(other) != 3:
            raise ValueError("Cross product is only defined for 3-dimensional vectors")
        return Vector([
            self[1] * other[2] - self[2] * other[1],
            self[2] * other[0] - self[0] * other[2],
            self[0] * other[1] - self[1] * other[0]
        ])

    def dot(self, other):
        return self * other

    def norm(self):
        return math.sqrt(sum([e ** 2 for e in self._values]))

使用示例：

v1 = Vector([1, 2, 3])
v2 = Vector([1, 2, 3])
v3 = Vector([4, 5, 6])

print(v1 == v2)  # True
print(v1 == v3)  # False

print(v1 + v3)   # Vector([5, 7, 9])
print(v1 - v3)   # Vector([-3, -3, -3])
print(v1 * 2)    # Vector([2, 4, 6])
print(v1 / 2)    # Vector([0.5, 1.0, 1.5])

print(v1.dot(v3))   # 32
print(v1.cross(v3)) # Vector([-3, 6, -3])

print(v1.norm())    # 3.7416573867739413