update

classes/multivector_v1.py

@@ -0,0 +1,124 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 1
+
+A ``MultiVector`` is built from an iterable of numbers::
+
+    >>> MultiVector([3.1, 4.2])
+    MultiVector([3.1, 4.2])
+    >>> MultiVector((3, 4, 5))
+    MultiVector([3.0, 4.0, 5.0])
+    >>> MultiVector(range(10))
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([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(MultiVector([0, 0, 0]))
+    (True, False)
+
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+
+"""
+
+# BEGIN MULTIVECTOR_V1
+from array import array
+import reprlib
+import math
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(MultiVector.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 'MultiVector({})'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return 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):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)  # <7>
+# END MULTIVECTOR_V1

classes/multivector_v1_hash.py

@@ -0,0 +1,123 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 1
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([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(MultiVector([0, 0, 0]))
+    (True, False)
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, 5.0, 6.0])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+Tests of hashing::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> v2 = MultiVector([3.1, 4.2])
+    >>> v3 = MultiVector([3, 4, 5])
+    >>> v4 = MultiVector(range(10))
+    >>> hash(v1), hash(v2), hash(v3), hash(v4)
+    (7, 384307168202284039, 2, 1)
+    >>> len(set([v1, v2, v3, v4]))
+    4
+
+
+"""
+
+from array import array
+import math
+import functools
+import operator
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(MultiVector.typecode, components)
+
+    def __iter__(self):
+        return iter(self._components)
+
+    def __repr__(self):
+        components = ', '.join(repr(x) for x in self)
+        return 'MultiVector([{}])'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return bytes(self._components)
+
+    def __eq__(self, other):
+        return tuple(self) == tuple(other)
+
+    def __hash__(self):
+        hashes = (hash(x) for x in self)
+        return functools.reduce(operator.xor, hashes)
+
+    def __abs__(self):
+        return math.sqrt(sum(x * x for x in self))
+
+    def __bool__(self):
+        return bool(abs(self))
+
+    @classmethod
+    def frombytes(cls, octets):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)

classes/multivector_v2.py

@@ -0,0 +1,164 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 2
+
+A ``MultiVector`` is built from an iterable of numbers::
+
+    >>> MultiVector([3.1, 4.2])
+    MultiVector([3.1, 4.2])
+    >>> MultiVector((3, 4, 5))
+    MultiVector([3.0, 4.0, 5.0])
+    >>> MultiVector(range(10))
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([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(MultiVector([0, 0, 0]))
+    (True, False)
+
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests of sequence behavior::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> len(v1)
+    3
+    >>> v1[0], v1[len(v1)-1], v1[-1]
+    (3.0, 5.0, 5.0)
+
+
+Test of slicing::
+
+# BEGIN MULTIVECTOR_V2_DEMO
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7[-1]  # <1>
+    6.0
+    >>> v7[1:4]  # <2>
+    MultiVector([1.0, 2.0, 3.0])
+    >>> v7[-1:]  # <3>
+    MultiVector([6.0])
+    >>> v7[1,2]  # <4>
+    Traceback (most recent call last):
+      ...
+    TypeError: MultiVector indices must be integers
+
+# END MULTIVECTOR_V2_DEMO
+
+"""
+
+from array import array
+import reprlib
+import math
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(MultiVector.typecode, components)
+
+    def __iter__(self):
+        return iter(self._components)
+
+    def __repr__(self):
+        components = reprlib.repr(self._components)
+        components = components[components.find('['):-1]
+        return 'MultiVector({})'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return 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 MULTIVECTOR_V2
+    def __len__(self):
+        return len(self._components)
+
+    def __getitem__(self, index):
+        cls = type(self)  # <1>
+        if isinstance(index, slice):
+            return cls(self._components[index])  # <2>
+        elif isinstance(index, int):
+            return self._components[index]  # <3>
+        else:
+            msg = '{cls.__name__} indices must be integers'
+            raise TypeError(msg.format(cls=cls))  # <4>
+# END MULTIVECTOR_V2
+
+    @classmethod
+    def frombytes(cls, octets):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)

classes/multivector_v3.py

@@ -0,0 +1,198 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 2
+
+A ``MultiVector`` is built from an iterable of numbers::
+
+    >>> MultiVector([3.1, 4.2])
+    MultiVector([3.1, 4.2])
+    >>> MultiVector((3, 4, 5))
+    MultiVector([3.0, 4.0, 5.0])
+    >>> MultiVector(range(10))
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([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(MultiVector([0, 0, 0]))
+    (True, False)
+
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests of sequence behavior::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> len(v1)
+    3
+    >>> v1[0], v1[len(v1)-1], v1[-1]
+    (3.0, 5.0, 5.0)
+
+
+Test of slicing::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7[-1]
+    6.0
+    >>> v7[1:4]
+    MultiVector([1.0, 2.0, 3.0])
+    >>> v7[-1:]
+    MultiVector([6.0])
+    >>> v7[1,2]
+    Traceback (most recent call last):
+      ...
+    TypeError: MultiVector indices must be integers
+
+
+Tests of dynamic attribute access::
+
+    >>> v7 = MultiVector(range(10))
+    >>> v7.x
+    0.0
+    >>> v7.y, v7.z, v7.t, v7.u, v7.v, v7.w
+    (1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+
+Dynamic attribute lookup failures::
+
+    >>> v7.k
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'k'
+    >>> v3 = MultiVector(range(3))
+    >>> v3.t
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 't'
+    >>> v3.spam
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'spam'
+
+
+"""
+
+from array import array
+import reprlib
+import math
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(MultiVector.typecode, components)
+
+    def __iter__(self):
+        return iter(self._components)
+
+    def __repr__(self):
+        components = reprlib.repr(self._components)
+        components = components[components.find('['):-1]
+        return 'MultiVector({})'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return 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, int):
+            return self._components[index]
+        else:
+            msg = '{.__name__} indices must be integers'
+            raise TypeError(msg.format(cls))
+
+# BEGIN MULTIVECTOR_V3
+    shortcut_names = 'xyztuvw'
+
+    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 MULTIVECTOR_V3
+
+    @classmethod
+    def frombytes(cls, octets):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)

classes/multivector_v4.py

@@ -0,0 +1,213 @@
+"""
+A multi-dimensional ``MultiVector`` class, take 2
+
+A ``MultiVector`` is built from an iterable of numbers::
+
+    >>> MultiVector([3.1, 4.2])
+    MultiVector([3.1, 4.2])
+    >>> MultiVector((3, 4, 5))
+    MultiVector([3.0, 4.0, 5.0])
+    >>> MultiVector(range(10))
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+
+
+Tests with 2-dimensions (same results as ``vector_v1.py``)::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> x, y = v1
+    >>> x, y
+    (3.0, 4.0)
+    >>> v1
+    MultiVector([3.0, 4.0])
+    >>> v1_clone = eval(repr(v1))
+    >>> v1 == v1_clone
+    True
+    >>> print(v1)
+    (3.0, 4.0)
+    >>> octets = bytes(v1)
+    >>> octets
+    b'\\x00\\x00\\x00\\x00\\x00\\x00\\x08@\\x00\\x00\\x00\\x00\\x00\\x00\\x10@'
+    >>> abs(v1)
+    5.0
+    >>> bool(v1), bool(MultiVector([0, 0]))
+    (True, False)
+
+
+Test of ``.frombytes()`` class method:
+
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests with 3-dimensions::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> x, y, z = v1
+    >>> x, y, z
+    (3.0, 4.0, 5.0)
+    >>> v1
+    MultiVector([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(MultiVector([0, 0, 0]))
+    (True, False)
+
+
+Tests with many dimensions::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7
+    MultiVector([0.0, 1.0, 2.0, 3.0, 4.0, ...])
+    >>> abs(v7)  # doctest:+ELLIPSIS
+    9.53939201...
+
+
+Test of ``.__bytes__`` and ``.frombytes()`` methods::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> v1_clone = MultiVector.frombytes(bytes(v1))
+    >>> v1_clone
+    MultiVector([3.0, 4.0, 5.0])
+    >>> v1 == v1_clone
+    True
+
+
+Tests of sequence behavior::
+
+    >>> v1 = MultiVector([3, 4, 5])
+    >>> len(v1)
+    3
+    >>> v1[0], v1[len(v1)-1], v1[-1]
+    (3.0, 5.0, 5.0)
+
+
+Test of slicing::
+
+    >>> v7 = MultiVector(range(7))
+    >>> v7[-1]
+    6.0
+    >>> v7[1:4]
+    MultiVector([1.0, 2.0, 3.0])
+    >>> v7[-1:]
+    MultiVector([6.0])
+    >>> v7[1,2]
+    Traceback (most recent call last):
+      ...
+    TypeError: MultiVector indices must be integers
+
+
+Tests of dynamic attribute access::
+
+    >>> v7 = MultiVector(range(10))
+    >>> v7.x
+    0.0
+    >>> v7.y, v7.z, v7.t, v7.u, v7.v, v7.w
+    (1.0, 2.0, 3.0, 4.0, 5.0, 6.0)
+
+Dynamic attribute lookup failures::
+
+    >>> v7.k
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'k'
+    >>> v3 = MultiVector(range(3))
+    >>> v3.t
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 't'
+    >>> v3.spam
+    Traceback (most recent call last):
+      ...
+    AttributeError: 'MultiVector' object has no attribute 'spam'
+
+
+Tests of hashing::
+
+    >>> v1 = MultiVector([3, 4])
+    >>> v2 = MultiVector([3.1, 4.2])
+    >>> v3 = MultiVector([3, 4, 5])
+    >>> v6 = MultiVector(range(6))
+    >>> hash(v1), hash(v2), hash(v3), hash(v6)
+    (7, 384307168202284039, 2, 1)
+    >>> len(set([v1, v2, v3, v6]))
+    4
+
+
+"""
+
+from array import array
+import reprlib
+import math
+import functools
+import operator
+
+
+class MultiVector:
+    typecode = 'd'
+
+    def __init__(self, components):
+        self._components = array(MultiVector.typecode, components)
+
+    def __iter__(self):
+        return iter(self._components)
+
+    def __repr__(self):
+        components = reprlib.repr(self._components)
+        components = components[components.find('['):-1]
+        return 'MultiVector({})'.format(components)
+
+    def __str__(self):
+        return str(tuple(self))
+
+    def __bytes__(self):
+        return bytes(self._components)
+
+    def __eq__(self, other):
+        return tuple(self) == tuple(other)
+
+    def __hash__(self):
+        hashes = (hash(x) for x in self)
+        return functools.reduce(operator.xor, hashes)
+
+    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, int):
+            return self._components[index]
+        else:
+            msg = '{.__name__} indices must be integers'
+            raise TypeError(msg.format(cls))
+
+    shortcut_names = 'xyztuvw'
+
+    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))
+
+    @classmethod
+    def frombytes(cls, octets):
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(memv)

classes/vector_v1.py

@@ -80,7 +80,6 @@ class Vector:
 # BEGIN VECTOR_V1
     @classmethod  # <1>
     def frombytes(cls, octets):  # <2>
-        arr = array(Vector.typecode)  # <3>
-        arr.frombytes(octets)  # <4>
-        return cls(*arr)  # <5>
+        memv = memoryview(octets).cast(cls.typecode)  # <3>
+        return cls(*memv)  # <4>
 # END VECTOR_V1

classes/vector_v2.py

@@ -108,6 +108,5 @@ class Vector:
 
     @classmethod
     def frombytes(cls, octets):
-        arr = array(Vector.typecode)
-        arr.frombytes(octets)
-        return cls(*arr)
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(*memv)

classes/vector_v2_fmt_snippet.py

@@ -110,6 +110,5 @@ class Vector:
 
     @classmethod
     def frombytes(cls, octets):
-        arr = array(Vector.typecode)
-        arr.frombytes(octets)
-        return cls(*arr)
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(*memv)

classes/vector_v3.py

@@ -46,8 +46,9 @@ Test of `x` and `y` read-only properties:
     >>> v2 = Vector(3.1, 4.2)
     >>> hash(v1), hash(v2)
     (7, 384307168202284039)
-    >>> set([v1, v2])
-    {Vector(3.1, 4.2), Vector(3.0, 4.0)}
+    >>> len(set([v1, v2]))
+    2
+
 
 # END VECTOR_V3_DEMO
 
@@ -118,6 +119,5 @@ class Vector:
 
     @classmethod
     def frombytes(cls, octets):
-        arr = array(Vector.typecode)
-        arr.frombytes(octets)
-        return cls(*arr)
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(*memv)

classes/vector_v3_slots.py

@@ -46,8 +46,8 @@ Test of `x` and `y` read-only properties:
     >>> v2 = Vector(3.1, 4.2)
     >>> hash(v1), hash(v2)
     (7, 384307168202284039)
-    >>> set([v1, v2])
-    {Vector(3.1, 4.2), Vector(3.0, 4.0)}
+    >>> len(set([v1, v2]))
+    2
 
 # END VECTOR_V3_DEMO
 
@@ -120,6 +120,5 @@ class Vector:
 
     @classmethod
     def frombytes(cls, octets):
-        arr = array(Vector.typecode)
-        arr.frombytes(octets)
-        return cls(*arr)
+        memv = memoryview(octets).cast(cls.typecode)
+        return cls(*memv)