Factory for cached representations

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.


  • 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.


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.


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.


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.


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.finite_field_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

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)

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)

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
sage: hasattr(c, '_factory_data')

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)

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
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)
sage: loads(dumps(e)) is e
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.


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().


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.


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).


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', {})
sage: test_factory.get_object(3.0, 'a', {}) is test_factory.get_object(3.1, 'a', {})
Making object a
sage: test_factory.get_object(3.0, 'a', {}) is test_factory.get_object(3.0, 'b', {})
Making object b

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.


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.


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

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.


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

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.


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


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

Used in unpickling the factory itself.


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.