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# Factory for cached representations

Factory for cached representations

See also

`sage.structure.unique_representation`

Using a `UniqueFactory` is one way of implementing a cached representation behaviour. In spite of its name, using a `UniqueFactory` is not enough to ensure the unique representation behaviour. See `unique_representation` for a detailed explanation.

With a `UniqueFactory`, one can preprocess the given arguments. There is special support for specifying a subset of the arguments that serve as the unique key, so that still all given arguments are used to create a new instance, but only the specified subset is used to look up in the cache. Typically, this is used to construct objects that accept an optional `check=[True|False]` argument, but whose result should be unique regardless of said optional argument. (This use case should be handled with care, though: Any checking which isn’t done in the `create_key` or `create_key_and_extra_args` method will be done only when a new object is generated, but not when a cached object is retrieved from cache. Consequently, if the factory is once called with `check=False`, a subsequent call with `check=True` cannot be expected to perform all checks unless these checks are all in the `create_key` or `create_key_and_extra_args` method.)

For a class derived from `CachedRepresentation`, argument preprocessing can be obtained by providing a custom static `__classcall__` or `__classcall_private__` method, but this seems less transparent. When argument preprocessing is not needed or the preprocess is not very sophisticated, then generally `CachedRepresentation` is much easier to use than a factory.

AUTHORS:

- Robert Bradshaw (2008): initial version.
- Simon King (2013): extended documentation.
- Julian Rueth (2014-05-09): use `_cache_key` if parameters are unhashable

class `sage.structure.factory.``UniqueFactory`

  Bases: `sage.structure.sage_object.SageObject`

  This class is intended to make it easy to cache objects.

  It is based on the idea that the object is uniquely defined by a set of defining data (the key). There is also the possibility of some non-defining data (extra args) which will be used in initial creation, but not affect the caching.

  Warning

  This class only provides cached representation behaviour. Hence, using `UniqueFactory`, it is still possible to create distinct objects that evaluate equal. Unique representation behaviour can be added, for example, by additionally inheriting from `sage.misc.fast_methods.WithEqualityById`.

  The objects created are cached (using weakrefs) based on their key and returned directly rather than re-created if requested again. Pickling is taken care of by the factory, and will return the same object for the same version of Sage, and distinct (but hopefully equal) objects for different versions of Sage.

  Warning

  The objects returned by a `UniqueFactory` must be instances of new style classes (hence, they must be instances of `object`) that must not only allow a weak reference, but must accept general attribute assignment. Otherwise, pickling won’t work.

  USAGE:

  A unique factory provides a way to create objects from parameters (the type of these objects can depend on the parameters, and is often determined only at runtime) and to cache them by a certain key derived from these parameters, so that when the factory is being called again with the same parameters (or just with parameters which yield the same key), the object is being returned from cache rather than constructed anew.

  An implementation of a unique factory consists of a factory class and an instance of this factory class.

  The factory class has to be a class inheriting from `UniqueFactory`. Typically it only needs to implement `create_key()` (a method that creates a key from the given parameters, under which key the object will be stored in the cache) and `create_object()` (a method that returns the actual object from the key). Sometimes, one would also implement `create_key_and_extra_args()` (this differs from `create_key()` in allowing to also create some additional arguments from the given parameters, which arguments then get passed to `create_object()` and thus can have an effect on the initial creation of the object, but do not affect the key) or `other_keys()`. Other methods are not supposed to be overloaded.

  The factory class itself cannot be called to create objects. Instead, an instance of the factory class has to be created first. For technical reasons, this instance has to be provided with a name that allows Sage to find its definition. Specifically, the name of the factory instance (or the full path to it, if it is not in the global namespace) has to be passed to the factory class as a string variable. So, if our factory class has been called `A` and is located in `sage/spam/battletoads.py`, then we need to define an instance (say, `B`) of `A` by writing `B = A("sage.spam.battletoads.B")` (or `B = A("B")` if this `B` will be imported into global namespace). This instance can then be used to create objects (by calling `B(*parameters)`).

  Notice that the objects created by the factory don’t inherit from the factory class. They do know about the factory that created them (this information, along with the keys under which this factory caches them, is stored in the `_factory_data` attributes of the objects), but not via inheritance.

  EXAMPLES:

  The below examples are rather artificial and illustrate particular aspects. For a “real-life” usage case of `UniqueFactory`, see the finite field factory in `sage.rings.finite_rings.constructor`.

  In many cases, a factory class is implemented by providing the two methods `create_key()` and `create_object()`. In our example, we want to demonstrate how to use “extra arguments” to choose a specific implementation, with preference given to an instance found in the cache, even if its implementation is different. Hence, we implement `create_key_and_extra_args()` rather than `create_key()`, putting the chosen implementation into the extra arguments. Then, in the `create_object()` method, we create and return instances of the specified implementation.

      sage: from sage.structure.factory import UniqueFactory
      sage: class MyFactory(UniqueFactory):
      ....:     def create_key_and_extra_args(self, *args, **kwds):
      ....:         return args, {'impl':kwds.get('impl', None)}
      ....:     def create_object(self, version, key, **extra_args):
      ....:         impl = extra_args['impl']
      ....:         if impl=='C':
      ....:             return C(*key)
      ....:         if impl=='D':
      ....:             return D(*key)
      ....:         return E(*key)
      ....:

  Now we can create a factory instance. It is supposed to be found under the name `"F"` in the `"__main__"` module. Note that in an interactive session, `F` would automatically be in the `__main__` module. Hence, the second and third of the following four lines are only needed in doctests.

      sage: F = MyFactory("__main__.F")
      sage: import __main__
      sage: __main__.F = F
      sage: loads(dumps(F)) is F
      True

  Now we create three classes `C`, `D` and `E`. The first is a Cython extension-type class that does not allow weak references nor attribute assignment. The second is a Python class that is not derived from `object`. The third allows attribute assignment and is derived from `object`.

      sage: cython("cdef class C: pass")
      sage: class D:
      ....:     def __init__(self, *args):
      ....:         self.t = args
      ....:     def __repr__(self):
      ....:         return "D%s"%repr(self.t)
      ....:
      sage: class E(D, object): pass

  Again, being in a doctest, we need to put the class `D` into the `__main__` module, so that Python can find it:

      sage: import __main__
      sage: __main__.D = D

  It is impossible to create an instance of `C` with our factory, since it does not allow weak references:

      sage: F(1, impl='C')
      Traceback (most recent call last):
      ...
      TypeError: cannot create weak reference to '....C' object

  Let us try again, with a Cython class that does allow weak references. Now, creation of an instance using the factory works:

      sage: cython('''cdef class C:
      ....:     cdef __weakref__
      ....: ''')
      ....:
      sage: c = F(1, impl='C')
      sage: isinstance(c, C)
      True

  The cache is used when calling the factory again—even if it is suggested to use a different implementation. This is because the implementation is only considered an “extra argument” that does not count for the key.

      sage: c is F(1, impl='C') is F(1, impl="D") is F(1)
      True

  However, pickling and unpickling does not use the cache. This is because the factory has tried to assign an attribute to the instance that provides information on the key used to create the instance, but failed:

      sage: loads(dumps(c)) is c
      False
      sage: hasattr(c, '_factory_data')
      False

  We have already seen that our factory will only take the requested implementation into account if the arguments used as key have not been used yet. So, we use other arguments to create an instance of class `D`:

      sage: d = F(2, impl='D')
      sage: isinstance(d, D)
      True

  The factory only knows about the pickling protocol used by new style classes. Hence, again, pickling and unpickling fails to use the cache, even though the “factory data” are now available:

      sage: loads(dumps(d)) is d
      False
      sage: d._factory_data
      (<class '__main__.MyFactory'>, (...), (2,), {'impl': 'D'})

  Only when we have a new style class that can be weak referenced and allows for attribute assignment, everything works:

      sage: e = F(3)
      sage: isinstance(e, E)
      True
      sage: loads(dumps(e)) is e
      True
      sage: e._factory_data
      (<class '__main__.MyFactory'>, (...), (3,), {'impl': None})

  `create_key`(*args, **kwds)

    Given the parameters (arguments and keywords), create a key that uniquely determines this object.

    EXAMPLES:

        sage: from sage.structure.test_factory import test_factory
        sage: test_factory.create_key(1, 2, key=5)
        (1, 2)

  `create_key_and_extra_args`(*args, **kwds)

    Return a tuple containing the key (uniquely defining data) and any extra arguments (empty by default).

    Defaults to `create_key()`.

    EXAMPLES:

        sage: from sage.structure.test_factory import test_factory
        sage: test_factory.create_key_and_extra_args(1, 2, key=5)
        ((1, 2), {})
        sage: GF.create_key_and_extra_args(3, foo='value')
        ((3, ('x',), None, 'modn', "{'foo': 'value'}", 3, 1, True), {'foo': 'value'})

  `create_object`(version, key, **extra_args)

    Create the object from the key and extra arguments. This is only called if the object was not found in the cache.

    EXAMPLES:

        sage: from sage.structure.test_factory import test_factory
        sage: test_factory.create_object(0, (1,2,3))
        Making object (1, 2, 3)
        <sage.structure.test_factory.A instance at ...>
        sage: test_factory('a')
        Making object ('a',)
        <sage.structure.test_factory.A instance at ...>
        sage: test_factory('a') # NOT called again
        <sage.structure.test_factory.A instance at ...>

  `get_object`(version, key, extra_args)

    Returns the object corresponding to `key`, creating it with `extra_args` if necessary (for example, it isn’t in the cache or it is unpickling from an older version of Sage).

    EXAMPLES:

        sage: from sage.structure.test_factory import test_factory
        sage: a = test_factory.get_object(3.0, 'a', {}); a
        Making object a
        <sage.structure.test_factory.A instance at ...>
        sage: test_factory.get_object(3.0, 'a', {}) is test_factory.get_object(3.0, 'a', {})
        True
        sage: test_factory.get_object(3.0, 'a', {}) is test_factory.get_object(3.1, 'a', {})
        Making object a
        False
        sage: test_factory.get_object(3.0, 'a', {}) is test_factory.get_object(3.0, 'b', {})
        Making object b
        False

    TESTS:

    Check that trac ticket #16317 has been fixed, i.e., caching works for unhashable objects:

        sage: K.<u> = Qq(4)
        sage: test_factory.get_object(3.0, (K(1), 'c'), {})  is test_factory.get_object(3.0, (K(1), 'c'), {})
        Making object (1 + O(2^20), 'c')
        True

  `get_version`(sage_version)

    This is provided to allow more or less granular control over pickle versioning. Objects pickled in the same version of Sage will unpickle to the same rather than simply equal objects. This can provide significant gains as arithmetic must be performed on objects with identical parents. However, if there has been an incompatible change (e.g. in element representation) we want the version number to change so coercion is forced between the two parents.

    Defaults to the Sage version that is passed in, but coarser granularity can be provided.

    EXAMPLES:

        sage: from sage.structure.test_factory import test_factory
        sage: test_factory.get_version((3,1,0))
        (3, 1, 0)

  `other_keys`(key, obj)

    Sometimes during object creation, certain defaults are chosen which may result in a new (more specific) key. This allows the more specific key to be regarded as equivalent to the original key returned by `create_key()` for the purpose of lookup in the cache, and is used for pickling.

    EXAMPLES:

    The `GF` factory used to have a custom `other_keys()` method, but this was removed in trac ticket #16934:

        sage: key, _ = GF.create_key_and_extra_args(27, 'k'); key
        (27, ('k',), x^3 + 2*x + 1, 'givaro', '{}', 3, 3, True)
        sage: K = GF.create_object(0, key); K
        Finite Field in k of size 3^3
        sage: GF.other_keys(key, K)
        []

        sage: K = GF(7^40, 'a')
        sage: loads(dumps(K)) is K
        True

  `reduce_data`(obj)

    The results of this function can be returned from `__reduce__()`. This is here so the factory internals can change without having to re-write `__reduce__()` methods that use it.

    EXAMPLE:

        sage: V = FreeModule(ZZ, 5)
        sage: factory, data = FreeModule.reduce_data(V)
        sage: factory(*data)
        Ambient free module of rank 5 over the principal ideal domain Integer Ring
        sage: factory(*data) is V
        True

        sage: from sage.structure.test_factory import test_factory
        sage: a = test_factory(1, 2)
        Making object (1, 2)
        sage: test_factory.reduce_data(a)
        (<built-in function generic_factory_unpickle>,
         (<class 'sage.structure.test_factory.UniqueFactoryTester'>,
          (...),
          (1, 2),
          {}))

    Note that the ellipsis `(...)` here stands for the Sage version.

`sage.structure.factory.``generic_factory_reduce`(self, proto)

  Used to provide a `__reduce__` method if one does not already exist.

  EXAMPLES:

      sage: V = QQ^6
      sage: sage.structure.factory.generic_factory_reduce(V, 1) == V.__reduce_ex__(1)
      True

`sage.structure.factory.``generic_factory_unpickle`(factory, *args)

  Method used for unpickling the object.

  The unpickling mechanism needs a plain Python function to call. It takes a factory as the first argument, passes the rest of the arguments onto the factory’s `UniqueFactory.get_object()` method.

  EXAMPLES:

      sage: V = FreeModule(ZZ, 5)
      sage: func, data = FreeModule.reduce_data(V)
      sage: func is sage.structure.factory.generic_factory_unpickle
      True
      sage: sage.structure.factory.generic_factory_unpickle(*data) is V
      True

  TESTS:

  The following was enabled in trac ticket #16349. Suppose we have defined (somewhere in the library of an old Sage version) a unique factory; in our example below, it returns polynomial rings. Now suppose that we want to replace the factory by something else, say, a class that provides the unique parent behaviour using `UniqueRepresentation`. We show here how to make it possible to unpickle a pickle created with the factory, automatically turning it into an instance of the new class.

  First, we create the factory. In a doctest, it is needed to explicitly put it into `__main__`, so that it can be located when pickling. Also, it is needed that we work with a new-style class:

      sage: from sage.structure.factory import UniqueFactory
      sage: import __main__
      sage: class OldStuff(object):
      ....:     def __init__(self, n, **extras):
      ....:         self.n = n
      ....:     def __repr__(self):
      ....:         return "Rotten old thing of level {}".format(self.n)
      sage: __main__.OldStuff = OldStuff
      sage: class MyFactory(UniqueFactory):
      ....:     def create_object(self, version, key, **extras):
      ....:         return OldStuff(key[0])
      ....:     def create_key(self, *args):
      ....:         return args
      sage: F = MyFactory('__main__.F')
      sage: __main__.F = F
      sage: a = F(3); a
      Rotten old thing of level 3
      sage: loads(dumps(a)) is a
      True

  Now, we create a pickle (the string returned by `dumps(a)`):

      sage: s = dumps(a)

  We create a new class, derived from `UniqueRepresentation`, that shall replace the old factory. In particular, the class has to have the same name as the old factory, and has to be put into the same module (here: `__main__`). We turn it into a sub-class of the old class, but this is just to save the effort of writing a new init method:

      sage: from sage.structure.unique_representation import UniqueRepresentation
      sage: class F(UniqueRepresentation, OldStuff):
      ....:     def __repr__(self):
      ....:         return "Shiny new thing of level {}".format(self.n)
      sage: __main__.F = F

  The old pickle correctly unpickles as an instance of the new class, which is of course different from the instance of the old class, but exhibits unique object behaviour as well:

      sage: b = loads(s); b
      Shiny new thing of level 3
      sage: a is b
      False
      sage: loads(dumps(b)) is b
      True

`sage.structure.factory.``lookup_global`(name)

  Used in unpickling the factory itself.

  EXAMPLES:

      sage: from sage.structure.factory import lookup_global
      sage: lookup_global('ZZ')
      Integer Ring
      sage: lookup_global('sage.rings.all.ZZ')
      Integer Ring

`sage.structure.factory.``register_factory_unpickle`(name, callable)

  Register a callable to handle the unpickling from an old `UniqueFactory` object.

  `UniqueFactory` pickles use a global name through `generic_factory_unpickle()`, so the usual `register_unpickle_override()` cannot be used here.

  See also

  `generic_factory_unpickle()`

  TESTS:

  This is similar to the example given in `generic_factory_unpickle()`, but here we will use a function to explicitly return a polynomial ring.

  First, we create the factory. In a doctest, it is needed to explicitly put it into `__main__`, so that it can be located when pickling. Also, it is needed that we work with a new-style class:

      sage: from sage.structure.factory import UniqueFactory, register_factory_unpickle
      sage: import __main__
      sage: class OldStuff(object):
      ....:     def __init__(self, n, **extras):
      ....:         self.n = n
      ....:     def __repr__(self):
      ....:         return "Rotten old thing of level {}".format(self.n)
      sage: __main__.OldStuff = OldStuff
      sage: class MyFactory(UniqueFactory):
      ....:     def create_object(self, version, key, **extras):
      ....:         return OldStuff(key[0])
      ....:     def create_key(self, *args):
      ....:         return args
      sage: G = MyFactory('__main__.G')
      sage: __main__.G = G
      sage: a = G(3); a
      Rotten old thing of level 3
      sage: loads(dumps(a)) is a
      True

  Now, we create a pickle (the string returned by `dumps(a)`):

      sage: s = dumps(a)

  We create the function which will handle the unpickling:

      sage: def foo(n, **kwds):
      ....:     return PolynomialRing(QQ, n, 'x')
      sage: register_factory_unpickle('__main__.G', foo)

  The old pickle correctly unpickles as an explicit polynomial ring:

      sage: loads(s)
      Multivariate Polynomial Ring in x0, x1, x2 over Rational Field

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