Factory for cached representations¶
See also
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=[TrueFalse]
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 (20140509): 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 nondefining 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 fromsage.misc.fast_methods.WithEqualityById
.The objects created are cached (using weakrefs) based on their key and returned directly rather than recreated 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 ofobject
) 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 implementcreate_key()
(a method that creates a key from the given parameters, under which key the object will be stored in the cache) andcreate_object()
(a method that returns the actual object from the key). Sometimes, one would also implementcreate_key_and_extra_args()
(this differs fromcreate_key()
in allowing to also create some additional arguments from the given parameters, which arguments then get passed tocreate_object()
and thus can have an effect on the initial creation of the object, but do not affect the key) orother_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 insage/spam/battletoads.py
, then we need to define an instance (say,B
) ofA
by writingB = A("sage.spam.battletoads.B")
(orB = A("B")
if thisB
will be imported into global namespace). This instance can then be used to create objects (by callingB(*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 “reallife” usage case of
UniqueFactory
, see the finite field factory insage.rings.finite_rings.finite_field_constructor
.In many cases, a factory class is implemented by providing the two methods
create_key()
andcreate_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 implementcreate_key_and_extra_args()
rather thancreate_key()
, putting the chosen implementation into the extra arguments. Then, in thecreate_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
andE
. The first is a Cython extensiontype class that does not allow weak references nor attribute assignment. The second is a Python class that is not derived fromobject
. The third allows attribute assignment and is derived fromobject
.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) ((3, ('x',), None, 'modn', 3, 1, True, None, None, None), {})

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 withextra_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

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 customother_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, None, 'poly', 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 rewrite__reduce__()
methods that use it.EXAMPLES:
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) (<builtin 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

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 throughgeneric_factory_unpickle()
, so the usualregister_unpickle_override()
cannot be used here.See also