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A multi-dimensional ``Vector`` class, take 6: operator ``+``
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: 'tuple' object cannot be interpreted as an integer
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 hashing::
    >>> v1 = Vector([3, 4])
    >>> v2 = Vector([3.1, 4.2])
    >>> v3 = Vector([3, 4, 5])
    >>> v6 = Vector(range(6))
    >>> hash(v1), hash(v3), hash(v6)
    (7, 2, 1)
Most hash codes of non-integers vary from a 32-bit to 64-bit Python build::
    >>> import sys
    >>> hash(v2) == (384307168202284039 if sys.maxsize > 2**32 else 357915986)
Tests of ``format()`` with Cartesian coordinates in 2D::
    >>> v1 = Vector([3, 4])
    >>> format(v1)
    '(3.0, 4.0)'
    >>> format(v1, '.2f')
    '(3.00, 4.00)'
    >>> format(v1, '.3e')
    '(3.000e+00, 4.000e+00)'
Tests of ``format()`` with Cartesian coordinates in 3D and 7D::
    >>> v3 = Vector([3, 4, 5])
    >>> format(v3)
    '(3.0, 4.0, 5.0)'
    >>> format(Vector(range(7)))
    '(0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0)'
Tests of ``format()`` with spherical coordinates in 2D, 3D and 4D::
    >>> format(Vector([1, 1]), 'h')  # doctest:+ELLIPSIS
    '<1.414213..., 0.785398...>'
    >>> format(Vector([1, 1]), '.3eh')
    '<1.414e+00, 7.854e-01>'
    >>> format(Vector([1, 1]), '0.5fh')
    '<1.41421, 0.78540>'
    >>> format(Vector([1, 1, 1]), 'h')  # doctest:+ELLIPSIS
    '<1.73205..., 0.95531..., 0.78539...>'
    >>> format(Vector([2, 2, 2]), '.3eh')
    '<3.464e+00, 9.553e-01, 7.854e-01>'
    >>> format(Vector([0, 0, 0]), '0.5fh')
    '<0.00000, 0.00000, 0.00000>'
    >>> format(Vector([-1, -1, -1, -1]), 'h')  # doctest:+ELLIPSIS
    '<2.0, 2.09439..., 2.18627..., 3.92699...>'
    >>> format(Vector([2, 2, 2, 2]), '.3eh')
    '<4.000e+00, 1.047e+00, 9.553e-01, 7.854e-01>'
    >>> format(Vector([0, 1, 0, 0]), '0.5fh')
    '<1.00000, 1.57080, 0.00000, 0.00000>'
Unary operator tests::
    >>> v1 = Vector([3, 4])
    >>> abs(v1)
    >>> -v1
    Vector([-3.0, -4.0])
    >>> +v1
    Vector([3.0, 4.0])
Basic tests of operator ``+``::
    >>> v1 = Vector([3, 4, 5])
    >>> v2 = Vector([6, 7, 8])
    >>> v1 + v2
    Vector([9.0, 11.0, 13.0])
    >>> v1 + v2 == Vector([3+6, 4+7, 5+8])
    >>> v3 = Vector([1, 2])
    >>> v1 + v3  # short vectors are filled with 0.0 on addition
    Vector([4.0, 6.0, 5.0])
Tests of ``+`` with mixed types::
    >>> v1 + (10, 20, 30)
    Vector([13.0, 24.0, 35.0])
    >>> from vector2d_v3 import Vector2d
    >>> v2d = Vector2d(1, 2)
    >>> v1 + v2d
    Vector([4.0, 6.0, 5.0])
Tests of ``+`` with mixed types, swapped operands::
    >>> (10, 20, 30) + v1
    Vector([13.0, 24.0, 35.0])
    >>> from vector2d_v3 import Vector2d
    >>> v2d = Vector2d(1, 2)
    >>> v2d + v1
    Vector([4.0, 6.0, 5.0])
Tests of ``+`` with an unsuitable operand:
    >>> v1 + 1
    Traceback (most recent call last):
    TypeError: unsupported operand type(s) for +: 'Vector' and 'int'
    >>> v1 + 'ABC'
    Traceback (most recent call last):
    TypeError: unsupported operand type(s) for +: 'Vector' and 'str'
from array import array
import reprlib
import math
import functools
import operator
import itertools
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 f'Vector({components})'
    def __str__(self):
        return str(tuple(self))
    def __bytes__(self):
        return (bytes([ord(self.typecode)]) +
                bytes(self._components))
    def __eq__(self, other):
        return (len(self) == len(other) and
                all(a == b for a, b in zip(self, other)))
    def __hash__(self):
        hashes = (hash(x) for x in self)
        return functools.reduce(operator.xor, hashes, 0)
# tag::VECTOR_V6_UNARY[]
    def __abs__(self):
        return math.hypot(*self)
    def __neg__(self):
        return Vector(-x for x in self)  # <1>
    def __pos__(self):
        return Vector(self)  # <2>
# end::VECTOR_V6_UNARY[]
    def __bool__(self):
        return bool(abs(self))
    def __len__(self):
        return len(self._components)
    def __getitem__(self, key):
        if isinstance(key, slice):
            cls = type(self)
            return cls(self._components[key])
        index = operator.index(key)
        return self._components[index]
    __match_args__ = ('x', 'y', 'z', 't')
    def __getattr__(self, name):
        cls = type(self)
        try:
            pos = cls.__match_args__.index(name)
        except ValueError:
            pos = -1
        if 0 <= pos < len(self._components):
            return self._components[pos]
        msg = f'{cls.__name__!r} object has no attribute {name!r}'
        raise AttributeError(msg)
    def angle(self, n):
        r = math.hypot(*self[n:])
        a = math.atan2(r, self[n-1])
        if (n == len(self) - 1) and (self[-1] < 0):
            return math.pi * 2 - a
        else:
            return a
    def angles(self):
        return (self.angle(n) for n in range(1, len(self)))
    def __format__(self, fmt_spec=''):
        if fmt_spec.endswith('h'):  # hyperspherical coordinates
            fmt_spec = fmt_spec[:-1]
            coords = itertools.chain([abs(self)],
                                     self.angles())
            outer_fmt = '<{}>'
        else:
            coords = self
            outer_fmt = '({})'
        components = (format(c, fmt_spec) for c in coords)
        return outer_fmt.format(', '.join(components))
    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)
# tag::VECTOR_V6_ADD[]
    def __add__(self, other):
        try:
            pairs = itertools.zip_longest(self, other, fillvalue=0.0)
            return Vector(a + b for a, b in pairs)
        except TypeError:
            return NotImplemented
    def __radd__(self, other):
        return self + other
# end::VECTOR_V6_ADD[]
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