Singleton categories¶
-
class
sage.categories.category_singleton.
Category_contains_method_by_parent_class
¶ Bases:
object
Returns whether
x
is an object in this category.More specifically, returns
True
if and only ifx
has a category which is a subcategory of this one.EXAMPLES:
sage: ZZ in Sets() True
-
class
sage.categories.category_singleton.
Category_singleton
(s=None)¶ Bases:
sage.categories.category.Category
A base class for implementing singleton category
A singleton category is a category whose class takes no parameters like
Fields()
orRings()
. See also the Singleton design pattern.This is a subclass of
Category
, with a couple optimizations for singleton categories.The main purpose is to make the idioms:
sage: QQ in Fields() True sage: ZZ in Fields() False
as fast as possible, and in particular competitive to calling a constant Python method, in order to foster its systematic use throughout the Sage library. Such tests are time critical, in particular when creating a lot of polynomial rings over small fields like in the elliptic curve code.
EXAMPLES:
sage: from sage.categories.category_singleton import Category_singleton sage: class MyRings(Category): ....: def super_categories(self): return Rings().super_categories() sage: class MyRingsSingleton(Category_singleton): ....: def super_categories(self): return Rings().super_categories()
We create three rings. One of them is contained in the usual category of rings, one in the category of “my rings” and the third in the category of “my rings singleton”:
sage: R = QQ['x,y'] sage: R1 = Parent(category = MyRings()) sage: R2 = Parent(category = MyRingsSingleton()) sage: R in MyRings() False sage: R1 in MyRings() True sage: R1 in MyRingsSingleton() False sage: R2 in MyRings() False sage: R2 in MyRingsSingleton() True
One sees that containment tests for the singleton class is a lot faster than for a usual class:
sage: timeit("R in MyRings()", number=10000) # not tested 10000 loops, best of 3: 7.12 µs per loop sage: timeit("R1 in MyRings()", number=10000) # not tested 10000 loops, best of 3: 6.98 µs per loop sage: timeit("R in MyRingsSingleton()", number=10000) # not tested 10000 loops, best of 3: 3.08 µs per loop sage: timeit("R2 in MyRingsSingleton()", number=10000) # not tested 10000 loops, best of 3: 2.99 µs per loop
So this is an improvement, but not yet competitive with a pure Cython method:
sage: timeit("R.is_ring()", number=10000) # not tested 10000 loops, best of 3: 383 ns per loop
However, it is competitive with a Python method. Actually it is faster, if one stores the category in a variable:
sage: _Rings = Rings() sage: R3 = Parent(category = _Rings) sage: R3.is_ring.__module__ 'sage.categories.rings' sage: timeit("R3.is_ring()", number=10000) # not tested 10000 loops, best of 3: 2.64 µs per loop sage: timeit("R3 in Rings()", number=10000) # not tested 10000 loops, best of 3: 3.01 µs per loop sage: timeit("R3 in _Rings", number=10000) # not tested 10000 loops, best of 3: 652 ns per loop
This might not be easy to further optimize, since the time is consumed in many different spots:
sage: timeit("MyRingsSingleton.__classcall__()", number=10000)# not tested 10000 loops, best of 3: 306 ns per loop sage: X = MyRingsSingleton() sage: timeit("R in X ", number=10000) # not tested 10000 loops, best of 3: 699 ns per loop sage: c = MyRingsSingleton().__contains__ sage: timeit("c(R)", number = 10000) # not tested 10000 loops, best of 3: 661 ns per loop
Warning
A singleton concrete class \(A\) should not have a subclass \(B\) (necessarily concrete). Otherwise, creating an instance \(a\) of \(A\) and an instance \(b\) of \(B\) would break the singleton principle: \(A\) would have two instances \(a\) and \(b\).
With the current implementation only direct subclasses of
Category_singleton
are supported:sage: class MyRingsSingleton(Category_singleton): ....: def super_categories(self): return Rings().super_categories() sage: class Disaster(MyRingsSingleton): pass sage: Disaster() Traceback (most recent call last): ... AssertionError: <class '__main__.Disaster'> is not a direct subclass of <class 'sage.categories.category_singleton.Category_singleton'>
However, it is acceptable for a direct subclass \(R\) of
Category_singleton
to create its unique instance as an instance of a subclass of itself (in which case, its the subclass of \(R\) which is concrete, not \(R\) itself). This is used for example to plug in extra category code via a dynamic subclass:sage: from sage.categories.category_singleton import Category_singleton sage: class R(Category_singleton): ....: def super_categories(self): return [Sets()] sage: R() Category of r sage: R().__class__ <class '__main__.R_with_category'> sage: R().__class__.mro() [<class '__main__.R_with_category'>, <class '__main__.R'>, <class 'sage.categories.category_singleton.Category_singleton'>, <class 'sage.categories.category.Category'>, <class 'sage.structure.unique_representation.UniqueRepresentation'>, <class 'sage.structure.unique_representation.CachedRepresentation'>, <type 'sage.misc.fast_methods.WithEqualityById'>, <type 'sage.structure.sage_object.SageObject'>, <class '__main__.R.subcategory_class'>, <class 'sage.categories.sets_cat.Sets.subcategory_class'>, <class 'sage.categories.sets_with_partial_maps.SetsWithPartialMaps.subcategory_class'>, <class 'sage.categories.objects.Objects.subcategory_class'>, <... 'object'>] sage: R() is R() True sage: R() is R().__class__() True
In that case,
R
is an abstract class and has a single concrete subclass, so this does not break the Singleton design pattern.See also
Note
The
_test_category
test is failing becauseMyRingsSingleton()
is not a subcategory of the join of its super categories:sage: C = MyRingsSingleton() sage: C.super_categories() [Category of rngs, Category of semirings] sage: Rngs() & Semirings() Category of rings sage: C.is_subcategory(Rings()) False
Oh well; it’s not really relevant for those tests.