试图找出我出错的原因。我的数字介于-1和1之间，但仍然有错误。

数学域错误

有什么想法吗？

谢谢

from math import sqrt, acos, pi
from decimal import Decimal, getcontext

getcontext().prec = 30


class Vector(object):
    CANNOT_NORMALIZE_ZERO_VECTOR_MSG = 'Cannot normalize the zero vector'

    def __init__(self, coordinates):
        try:
            if not coordinates:
                raise ValueError
            self.coordinates = tuple([Decimal(x) for x in coordinates])
            self.dimension = len(self.coordinates)

        except ValueError:
            raise ValueError('The coordinates must be nonempty')

        except TypeError:
            raise TypeError('The coordinates must be an iterable')

    def __str__(self):
        return 'Vector: {}'.format(self.coordinates)

    def __eq__(self, v):
        return self.coordinates == v.coordinates

    def magnitude(self):
        coordinates_squared = [x ** 2 for x in self.coordinates]
        return sqrt(sum(coordinates_squared))

    def normalized(self):
        try:
            magnitude = self.magnitude()
            return self.times_scalar(Decimal(1.0 / magnitude))

        except ZeroDivisionError:
            raise Exception('Cannot normalize the zero vector')

    def plus(self, v):
        new_coordinates = [x + y for x, y in zip(self.coordinates, v.coordinates)]
        return Vector(new_coordinates)

    def minus(self, v):
        new_coordinates = [x - y for x, y in zip(self.coordinates, v.coordinates)]
        return Vector(new_coordinates)

    def times_scalar(self, c):
        new_coordinates = [Decimal(c) * x for x in self.coordinates]
        return Vector(new_coordinates)

    def dot(self, v):
        return sum([x * y for x, y in zip(self.coordinates, v.coordinates)])

    def angle_with(self, v, in_degrees=False):
        try:
            u1 = self.normalized()
            u2 = v.normalized()
            angle_in_radians = acos(u1.dot(u2))

            if in_degrees:
                degrees_per_radian = 180. / pi
                return angle_in_radians * degrees_per_radian
            else:
                return angle_in_radians

        except Exception as e:
            if str(e) == self.CANNOT_NORMALIZE_ZERO_VECTOR_MSG:
                raise Exception('Cannot comput an angle with a zero vector')
            else:
                raise e

    def is_orthogonal_to(self, v, tolerance=1e-10):
        return abs(self.dot(v)) < tolerance

    def is_parallel_to(self, v):
        return self.is_zero() or v.is_zero() or self.angle_with(v) == 0 or self.angle_with(v) == pi

    def is_zero(self, tolerance=1e-10):
        return self.magnitude() < tolerance


print('first pair...')
v = Vector(['-7.579', '-7.88'])
w = Vector(['22.737', '23.64'])
print('is parallel:', v.is_parallel_to(w))
print('is orthogonal:', v.is_orthogonal_to(w))

print('second pair...')
v = Vector(['-2.029', '9.97', '4.172'])
w = Vector(['-9.231', '-6.639', '-7.245'])
print('is parallel:', v.is_parallel_to(w))
print('is orthogonal:', v.is_orthogonal_to(w))

print('third pair...')
v = Vector(['-2.328', '-7.284', '-1.214'])
w = Vector(['-1.821', '1.072', '-2.94'])
print('is parallel:', v.is_parallel_to(w))
print('is orthogonal:', v.is_orthogonal_to(w))

print('fourth pair...')
v = Vector(['2.118', '4.827'])
w = Vector(['0', '0'])
print('is parallel:', v.is_parallel_to(w))
print('is orthogonal:', v.is_orthogonal_to(w))