Python defines a full vector class

first edition:

# BEGIN VECTOR_V1
from array import array
import reprlib
import math


class Vector:
    typecode = 'd'

    def __init__(self, components):
        self._components = array(self.typecode, components)  # <1>

    def __iter__(self):
        return iter(self._components)  # <2>

    def __repr__(self):
        components = reprlib.repr(self._components)  # <3>
        components = components[components.find('['):-1]  # <4>
        return 'Vector({})'.format(components)

    def __str__(self):
        return str(tuple(self))

    def __bytes__(self):
        return (bytes([ord(self.typecode)]) +
                bytes(self._components))  # <5>

    def __eq__(self, other):
        return tuple(self) == tuple(other)

    def __abs__(self):
        return math.sqrt(sum(x * x for x in self))  # <6>

    def __bool__(self):
        return bool(abs(self))

    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)  # <7>
# END VECTOR_V1

second edition: slicable sequence

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))

# BEGIN VECTOR_V2
    def __len__(self):
        return len(self._components)

    def __getitem__(self, index):
        cls = type(self)  # <1>
        if isinstance(index, slice):  # <2>
            return cls(self._components[index])  # <3>
        elif isinstance(index, numbers.Integral):  # <4>
            return self._components[index]  # <5>
        else:
            msg = '{cls.__name__} indices must be integers'
            raise TypeError(msg.format(cls=cls))  # <6>
# END VECTOR_V2

    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)

The biggest change in

V2 is the implementation of ___ and ___, thereby enabling slicing, both of which are also necessary for vector to behave as a sequence:

if [1:4] is used, a slice is returned. Slice is a built-in type. A review of the slice reveals that it has the start,stop, step data attributes, and the indices methods. In indices, given a sequence of len, indexes at the beginning and the end of an extension section marked with S, as well as the stride length, are computed. Indexes exceeding the boundary are truncated.

Vector version 3: dynamic access property

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)

, ___ getattr__ and ___ setattr__, the former is to get vector components and the latter is to protect the existing components. V.x cannot be directly assigned because x has become an attribute of v. The value of v.x has changed, but the value of v has not.

Vector iv: hashing and fast equivalence testing

from array import array
import reprlib
import math
import numbers
import functools
import operator


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 (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)

    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 = '{cls.__name__} indices must be integers'
            raise TypeError(msg.format(cls=cls))

    shortcut_names = 'xyzt'

    def __getattr__(self, name):
        cls = type(self)
        if len(name) == 1:
            pos = cls.shortcut_names.find(name)
            if 0 <= pos < len(self._components):
                return self._components[pos]
        msg = '{.__name__!r} object has no attribute {!r}'
        raise AttributeError(msg.format(cls, name))

    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)

fifth edition: format

# BEGIN VECTOR_V5
"""
A multi-dimensional ``Vector`` class, take 5

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)
    >>> v1
    Vector([3.0, 4.0])
    >>> v1_clone = eval(repr(v1))
    >>> v1 == v1_clone
    True
    >>> print(v1)
    (3.0, 4.0)
    >>> octets = bytes(v1)
    >>> octets
    b'd\\x00\\x00\\x00\\x00\\x00\\x00\\[email protected]\\x00\\x00\\x00\\x00\\x00\\x00\\[email protected]'
    >>> abs(v1)
    5.0
    >>> 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
    True


Tests with 3-dimensions::

    >>> v1 = Vector([3, 4, 5])
    >>> x, y, z = v1
    >>> x, y, z
    (3.0, 4.0, 5.0)
    >>> v1
    Vector([3.0, 4.0, 5.0])
    >>> v1_clone = eval(repr(v1))
    >>> v1 == v1_clone
    True
    >>> 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))
    >>> v7
    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
    True


Tests of sequence behavior::

    >>> v1 = Vector([3, 4, 5])
    >>> len(v1)
    3
    >>> v1[0], v1[len(v1)-1], v1[-1]
    (3.0, 5.0, 5.0)


Test of slicing::

    >>> v7 = Vector(range(7))
    >>> v7[-1]
    6.0
    >>> 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
    0.0
    >>> 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 values of non-integers vary from a 32-bit to 64-bit CPython build::

    >>> import sys
    >>> hash(v2) == (384307168202284039 if sys.maxsize > 2**32 else 357915986)
    True


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>'
"""

from array import array
import reprlib
import math
import numbers
import functools
import operator
import itertools  # <1>


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 (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)

    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))

    shortcut_names = 'xyzt'

    def __getattr__(self, name):
        cls = type(self)
        if len(name) == 1:
            pos = cls.shortcut_names.find(name)
            if 0 <= pos < len(self._components):
                return self._components[pos]
        msg = '{.__name__!r} object has no attribute {!r}'
        raise AttributeError(msg.format(cls, name))

    def angle(self, n):  # <2>
        r = math.sqrt(sum(x * x for x in 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):  # <3>
        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())  # <4>
            outer_fmt = '<{}>'  # <5>
        else:
            coords = self
            outer_fmt = '({})'  # <6>
        components = (format(c, fmt_spec) for c in coords)  # <7>
        return outer_fmt.format(', '.join(components))  # <8>

    @classmethod
    def frombytes(cls, octets):
        typecode = chr(octets[0])
        memv = memoryview(octets[1:]).cast(typecode)
        return cls(memv)
# END VECTOR_V5



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