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A multi-dimensional ``Vector`` class, take 3
A ``Vector`` is built from an iterable of numbers::
    >>> Vector([3.1, 4.2])
    Vector([3.1, 4.2])
    >>> Vector((3, 4, 5))
    Vector([3.0, 4.0, 5.0])
    >>> Vector(range(10))
    Vector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
Tests with 2-dimensions (same results as ``vector2d_v1.py``)::
    >>> v1 = Vector([3, 4])
    >>> x, y = v1
    >>> x, y
    (3.0, 4.0)
    Vector([3.0, 4.0])
    >>> v1_clone = eval(repr(v1))
    >>> v1 == v1_clone
    >>> print(v1)
    (3.0, 4.0)
    >>> octets = bytes(v1)
    >>> octets
    b'd\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
    >>> abs(v1)
    >>> bool(v1), bool(Vector([0, 0]))
    (True, False)
Test of ``.frombytes()`` class method:
    >>> v1_clone = Vector.frombytes(bytes(v1))
    >>> v1_clone
    Vector([3.0, 4.0])
    >>> v1 == v1_clone
Tests with 3-dimensions::
    >>> v1 = Vector([3, 4, 5])
    >>> x, y, z = v1
    >>> x, y, z
    (3.0, 4.0, 5.0)
    Vector([3.0, 4.0, 5.0])
    >>> v1_clone = eval(repr(v1))
    >>> v1 == v1_clone
    >>> print(v1)
    (3.0, 4.0, 5.0)
    >>> abs(v1)  # doctest:+ELLIPSIS
    7.071067811...
    >>> bool(v1), bool(Vector([0, 0, 0]))
    (True, False)
Tests with many dimensions::
    >>> v7 = Vector(range(7))
    Vector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
    >>> abs(v7)  # doctest:+ELLIPSIS
    9.53939201...
Test of ``.__bytes__`` and ``.frombytes()`` methods::
    >>> v1 = Vector([3, 4, 5])
    >>> v1_clone = Vector.frombytes(bytes(v1))
    >>> v1_clone
    Vector([3.0, 4.0, 5.0])
    >>> v1 == v1_clone
Tests of sequence behavior::
    >>> v1 = Vector([3, 4, 5])
    >>> len(v1)
    >>> v1[0], v1[len(v1)-1], v1[-1]
    (3.0, 5.0, 5.0)
Test of slicing::
    >>> v7 = Vector(range(7))
    >>> v7[-1]
    >>> v7[1:4]
    Vector([1.0, 2.0, 3.0])
    >>> v7[-1:]
    Vector([6.0])
    >>> v7[1,2]
    Traceback (most recent call last):
    TypeError: Vector indices must be integers
Tests of dynamic attribute access::
    >>> v7 = Vector(range(10))
    >>> v7.x
    >>> v7.y, v7.z, v7.t
    (1.0, 2.0, 3.0)
Dynamic attribute lookup failures::
    >>> v7.k
    Traceback (most recent call last):
    AttributeError: 'Vector' object has no attribute 'k'
    >>> v3 = Vector(range(3))
    >>> v3.t
    Traceback (most recent call last):
    AttributeError: 'Vector' object has no attribute 't'
    >>> v3.spam
    Traceback (most recent call last):
    AttributeError: 'Vector' object has no attribute 'spam'
Tests of preventing attributes from 'a' to 'z'::
    >>> v1.x = 7
    Traceback (most recent call last):
    AttributeError: readonly attribute 'x'
    >>> v1.w = 7
    Traceback (most recent call last):
    AttributeError: can't set attributes 'a' to 'z' in 'Vector'
Other attributes can be set::
    >>> v1.X = 'albatross'
    >>> v1.X
    'albatross'
    >>> v1.ni = 'Ni!'
    >>> v1.ni
from array import array
import reprlib
import math
import numbers
class Vector:
    typecode = 'd'
    def __init__(self, components):
        self._components = array(self.typecode, components)
    def __iter__(self):
        return iter(self._components)
    def __repr__(self):
        components = reprlib.repr(self._components)
        components = components[components.find('['):-1]
        return 'Vector({})'.format(components)
    def __str__(self):
        return str(tuple(self))
    def __bytes__(self):
        return (bytes([ord(self.typecode)]) +
                bytes(self._components))
    def __eq__(self, other):
        return tuple(self) == tuple(other)
    def __abs__(self):
        return math.sqrt(sum(x * x for x in self))
    def __bool__(self):
        return bool(abs(self))
    def __len__(self):
        return len(self._components)
    def __getitem__(self, index):
        cls = type(self)
        if isinstance(index, slice):
            return cls(self._components[index])
        elif isinstance(index, numbers.Integral):
            return self._components[index]
        else:
            msg = '{.__name__} indices must be integers'
            raise TypeError(msg.format(cls))
# BEGIN VECTOR_V3_GETATTR
    shortcut_names = 'xyzt'
    def __getattr__(self, name):
        cls = type(self)  # <1>
        if len(name) == 1:  # <2>
            pos = cls.shortcut_names.find(name)  # <3>
            if 0 <= pos < len(self._components):  # <4>
                return self._components[pos]
        msg = '{.__name__!r} object has no attribute {!r}'  # <5>
        raise AttributeError(msg.format(cls, name))
# END VECTOR_V3_GETATTR
# BEGIN VECTOR_V3_SETATTR
    def __setattr__(self, name, value):
        cls = type(self)
        if len(name) == 1:  # <1>
            if name in cls.shortcut_names:  # <2>
                error = 'readonly attribute {attr_name!r}'
            elif name.islower():  # <3>
                error = "can't set attributes 'a' to 'z' in {cls_name!r}"
            else:
                error = ''  # <4>
            if error:  # <5>
                msg = error.format(cls_name=cls.__name__, attr_name=name)
                raise AttributeError(msg)
        super().__setattr__(name, value)  # <6>
# END VECTOR_V3_SETATTR
    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)
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