Set factories¶
A set factory \(F\) is a device for constructing some Parent
\(P\) that models subsets of a big set \(S\). Typically, each such parent
is constructed as the subset of \(S\) of all elements satisfying a
certain collection of constraints \(cons\). In such a hierarchy of
subsets, one needs an easy and flexible control on how elements are
constructed. For example, one may want to construct the elements of
\(P\) in some subclass of the class of the elements of \(S\). On other
occasions, one also often needs \(P\) to be a facade parent, whose
elements are represented as elements of \(S\) (see
FacadeSets).
The role of a set factory is twofold:
- Manage a database of constructors for the different parents \(P = F(cons)\) depending on the various kinds of constraints \(cons\). Note: currently there is no real support for that. We are gathering use cases before fixing the interface. 
- Ensure that the elements \(e = P(...)\) created by the different parents follows a consistent policy concerning their class and parent. 
Basic usage: constructing parents through a factory
The file sage.structure.set_factories_example shows an example of a
SetFactory together with typical implementation. Note that the
written code is intentionally kept minimal, many things and in particular
several iterators could be written in a more efficient way.
Consider the set \(S\) of couples \((x,y)\) with \(x\) and \(y\) in \(I:=\{0,1,2,3,4\}\).
We represent an element of \(S\) as a 2-elements tuple, wrapped in a class
XYPair deriving from ElementWrapper.
You can create a XYPair with any
Parent:
sage: from sage.structure.set_factories import *
sage: from sage.structure.set_factories_example import *
sage: p = XYPair(Parent(), (0,1)); p
(0, 1)
>>> from sage.all import *
>>> from sage.structure.set_factories import *
>>> from sage.structure.set_factories_example import *
>>> p = XYPair(Parent(), (Integer(0),Integer(1))); p
(0, 1)
Now, given \((a, b)\in S\) we want to consider the following subsets of \(S\)
The constraints considered here are admittedly trivial. In a realistic example, there would be much more of them. And for some sets of constraints no good enumeration algorithms would be known.
In Sage, those sets are constructed by passing the constraints to the factory. We first create the set with no constraints at all:
sage: XYPairs
Factory for XY pairs
sage: S = XYPairs(); S.list()
[(0, 0), (1, 0), ..., (4, 0), (0, 1), (1, 1), ..., (3, 4), (4, 4)]
sage: S.cardinality()
25
>>> from sage.all import *
>>> XYPairs
Factory for XY pairs
>>> S = XYPairs(); S.list()
[(0, 0), (1, 0), ..., (4, 0), (0, 1), (1, 1), ..., (3, 4), (4, 4)]
>>> S.cardinality()
25
Let us construct \(S_2\), \(S^3\) and \(S_2^3\):
sage: Sx2 = XYPairs(x=2); Sx2.list()
[(2, 0), (2, 1), (2, 2), (2, 3), (2, 4)]
sage: Sy3 = XYPairs(y=3); Sy3.list()
[(0, 3), (1, 3), (2, 3), (3, 3), (4, 3)]
sage: S23 = XYPairs(x=2, y=3); S23.list()
[(2, 3)]
>>> from sage.all import *
>>> Sx2 = XYPairs(x=Integer(2)); Sx2.list()
[(2, 0), (2, 1), (2, 2), (2, 3), (2, 4)]
>>> Sy3 = XYPairs(y=Integer(3)); Sy3.list()
[(0, 3), (1, 3), (2, 3), (3, 3), (4, 3)]
>>> S23 = XYPairs(x=Integer(2), y=Integer(3)); S23.list()
[(2, 3)]
Set factories provide an alternative way to build subsets of an
already constructed set: each set constructed by a factory has a
method subset() which accept new
constraints. Sets constructed by the factory or the
subset() methods are identical:
sage: Sx2s = S.subset(x=2); Sx2 is Sx2s
True
sage: Sx2.subset(y=3) is S23
True
>>> from sage.all import *
>>> Sx2s = S.subset(x=Integer(2)); Sx2 is Sx2s
True
>>> Sx2.subset(y=Integer(3)) is S23
True
It is not possible to change an already given constraint:
sage: S23.subset(y=5)
Traceback (most recent call last):
...
ValueError: Duplicate value for constraints 'y': was 3 now 5
>>> from sage.all import *
>>> S23.subset(y=Integer(5))
Traceback (most recent call last):
...
ValueError: Duplicate value for constraints 'y': was 3 now 5
Constructing custom elements: policies
We now come to the point of factories: constructing custom elements. The
writer of XYPairs() decided that, by default,
the parents Sx2, Sy3 and S23 are facade for parent S. This
means that each element constructed by those subsets behaves as if they where
directly constructed by S itself:
sage: Sx2.an_element().parent()
AllPairs
sage: el = Sx2.an_element()
sage: el.parent() is S
True
sage: type(el) is S.element_class
True
>>> from sage.all import *
>>> Sx2.an_element().parent()
AllPairs
>>> el = Sx2.an_element()
>>> el.parent() is S
True
>>> type(el) is S.element_class
True
This is not always desirable. The device which decides how to construct an
element is called a policy (see SetFactoryPolicy). Each factory
should have a default policy. Here is the policy of
XYPairs():
sage: XYPairs._default_policy
Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())]
>>> from sage.all import *
>>> XYPairs._default_policy
Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())]
This means that with the current policy, the parent builds elements with class
XYPair and parent AllPairs which is itself constructed by calling the
factory XYPairs() with constraints (). There
is a lot of flexibility to change that. We now illustrate how to make a few
different choices.
1 - In a first use case, we want to add some methods to the constructed
elements. As illustration, we add here a new method sum which returns
\(x+y\). We therefore create a new class for the elements which inherits from
XYPair:
sage: class NewXYPair(XYPair):
....:     def sum(self):
....:         return sum(self.value)
>>> from sage.all import *
>>> class NewXYPair(XYPair):
...     def sum(self):
...         return sum(self.value)
Here is an instance of this class (with a dummy parent):
sage: el = NewXYPair(Parent(), (2,3))
sage: el.sum()
5
>>> from sage.all import *
>>> el = NewXYPair(Parent(), (Integer(2),Integer(3)))
>>> el.sum()
5
We now want to have subsets generating those new elements while still having a
single real parent (the one with no constraint) for each element. The
corresponding policy is called TopMostParentPolicy. It takes three
parameters:
- the factory; 
- the parameters for void constraint; 
- the class used for elements. 
Calling the factory with this policy returns a new set which builds its elements with the new policy:
sage: new_policy = TopMostParentPolicy(XYPairs, (), NewXYPair)
sage: NewS = XYPairs(policy=new_policy)
sage: el = NewS.an_element(); el
(0, 0)
sage: el.sum()
0
sage: el.parent() is NewS
True
sage: isinstance(el, NewXYPair)
True
>>> from sage.all import *
>>> new_policy = TopMostParentPolicy(XYPairs, (), NewXYPair)
>>> NewS = XYPairs(policy=new_policy)
>>> el = NewS.an_element(); el
(0, 0)
>>> el.sum()
0
>>> el.parent() is NewS
True
>>> isinstance(el, NewXYPair)
True
Newly constructed subsets inherit the policy:
sage: NewS2 = NewS.subset(x=2)
sage: el2 = NewS2.an_element(); el2
(2, 0)
sage: el2.sum()
2
sage: el2.parent() is NewS
True
>>> from sage.all import *
>>> NewS2 = NewS.subset(x=Integer(2))
>>> el2 = NewS2.an_element(); el2
(2, 0)
>>> el2.sum()
2
>>> el2.parent() is NewS
True
2 - In a second use case, we want the elements to remember which
parent created them. The corresponding policy is called
SelfParentPolicy. It takes only two parameters:
- the factory; 
- the class used for elements. 
Here is an example:
sage: selfpolicy = SelfParentPolicy(XYPairs, NewXYPair)
sage: SelfS = XYPairs(policy=selfpolicy)
sage: el = SelfS.an_element()
sage: el.parent() is SelfS
True
>>> from sage.all import *
>>> selfpolicy = SelfParentPolicy(XYPairs, NewXYPair)
>>> SelfS = XYPairs(policy=selfpolicy)
>>> el = SelfS.an_element()
>>> el.parent() is SelfS
True
Now all subsets are the parent of the elements that they create:
sage: SelfS2 = SelfS.subset(x=2)
sage: el2 = SelfS2.an_element()
sage: el2.parent() is NewS
False
sage: el2.parent() is SelfS2
True
>>> from sage.all import *
>>> SelfS2 = SelfS.subset(x=Integer(2))
>>> el2 = SelfS2.an_element()
>>> el2.parent() is NewS
False
>>> el2.parent() is SelfS2
True
3 - Finally, a common use case is to construct simple python object which are
not Sage sage.structure.Element. As an example, we show how to build
a parent TupleS which construct pairs as tuple. The corresponding policy
is called BareFunctionPolicy. It takes two parameters:
- the factory; 
- the function called to construct the elements. 
Here is how to do it:
sage: cons = lambda t, check: tuple(t) # ignore the check parameter
sage: tuplepolicy = BareFunctionPolicy(XYPairs, cons)
sage: P = XYPairs(x=2, policy=tuplepolicy)
sage: P.list()
[(2, 0), (2, 1), (2, 2), (2, 3), (2, 4)]
sage: el = P.an_element()
sage: type(el)
<... 'tuple'>
>>> from sage.all import *
>>> cons = lambda t, check: tuple(t) # ignore the check parameter
>>> tuplepolicy = BareFunctionPolicy(XYPairs, cons)
>>> P = XYPairs(x=Integer(2), policy=tuplepolicy)
>>> P.list()
[(2, 0), (2, 1), (2, 2), (2, 3), (2, 4)]
>>> el = P.an_element()
>>> type(el)
<... 'tuple'>
Here are the currently implemented policies:
- FacadeParentPolicy: reuse an existing parent together with its element_class
- TopMostParentPolicy: use a parent created by the factory itself and provide a class- Elementfor it. In this case, we need to specify the set of constraints which build this parent taking the ownership of all elements and the class which will be used for the- Element.
- SelfParentPolicy: provide systematically- Elementand element_class and ensure that the parent is- self.
- BareFunctionPolicy: instead of calling a class constructor element are passed to a function provided to the policy.
Todo
Generalize TopMostParentPolicy to be able to have several
topmost parents.
Technicalities: how policies inform parents
Parents built from factories should inherit from
ParentWithSetFactory. This class provide a few methods
related to factories and policies. The __init__ method of
ParentWithSetFactory must be provided with the set of
constraints and the policy. A parent built from a factory must create
elements through a call to the method _element_constructor_. The
current way in which policies inform parents how to builds their elements is
set by a few attributes. So the class must accept attribute
adding. The precise details of which attributes are set may be subject
to change in the future.
How to write a set factory
See also
set_factories_example for an example of a factory.
Here are the specifications:
A parent built from a factory should
- inherit from - ParentWithSetFactory. It should accept a- policyargument and pass it verbatim to the- __init__method of- ParentWithSetFactorytogether with the set of constraints;
- create its elements through calls to the method - _element_constructor_;
- define a method - ParentWithSetFactory.check_elementwhich checks if a built element indeed belongs to it. The method should accept an extra keyword parameter called- checkspecifying which level of check should be performed. It will only be called when- bool(check)evaluates to- True.
The constructor of the elements of a parent from a factory should:
- receive the parent as first mandatory argument; 
- accept an extra optional keyword parameter called - checkwhich is meant to tell if the input must be checked or not. The precise meaning of- checkis intentionally left vague. The only intent is that if- bool(check)evaluates to- False, no check is performed at all.
A factory should
- define a method - __call__which is responsible for calling the appropriate parent constructor given the constraints;
- define a method overloading - SetFactory.add_constraints()which is responsible of computing the union of two sets of constraints;
- optionally define a method or an attribute - _default_policypassed to the- ParentWithSetFactoryif no policy is given to the factory.
Todo
There is currently no support for dealing with sets of constraints. The set factory and the parents must cooperate to consistently handle them. More support, together with a generic mechanism to select the appropriate parent class from the constraints, will be added as soon as we have gathered sufficiently enough use-cases.
AUTHORS:
- Florent Hivert (2011-2012): initial revision 
- class sage.structure.set_factories.BareFunctionPolicy(factory, constructor)[source]¶
- Bases: - SetFactoryPolicy- Policy where element are constructed using a bare function. - INPUT: - factory– an instance of- SetFactory
- constructor– a function
 - Given a factory - Fand a function- c, returns a policy for parent- Pcreating element using the function- f.- EXAMPLES: - sage: from sage.structure.set_factories import BareFunctionPolicy sage: from sage.structure.set_factories_example import XYPairs sage: cons = lambda t, check: tuple(t) # ignore the check parameter sage: tuplepolicy = BareFunctionPolicy(XYPairs, cons) sage: P = XYPairs(x=2, policy=tuplepolicy) sage: el = P.an_element() sage: type(el) <... 'tuple'> - >>> from sage.all import * >>> from sage.structure.set_factories import BareFunctionPolicy >>> from sage.structure.set_factories_example import XYPairs >>> cons = lambda t, check: tuple(t) # ignore the check parameter >>> tuplepolicy = BareFunctionPolicy(XYPairs, cons) >>> P = XYPairs(x=Integer(2), policy=tuplepolicy) >>> el = P.an_element() >>> type(el) <... 'tuple'> - element_constructor_attributes(constraints)[source]¶
- Return the element constructor attributes as per - SetFactoryPolicy.element_constructor_attributes().- INPUT: - constraints– a bunch of constraints
 
 
- class sage.structure.set_factories.FacadeParentPolicy(factory, parent)[source]¶
- Bases: - SetFactoryPolicy- Policy for facade parent. - INPUT: - factory– an instance of- SetFactory
- parent– an instance of- Parent
 - Given a factory - Fand a class- E, returns a policy for parent- Pcreating elements as if they were created by- parent.- EXAMPLES: - sage: from sage.structure.set_factories import SelfParentPolicy, FacadeParentPolicy sage: from sage.structure.set_factories_example import XYPairs, XYPair - >>> from sage.all import * >>> from sage.structure.set_factories import SelfParentPolicy, FacadeParentPolicy >>> from sage.structure.set_factories_example import XYPairs, XYPair - We create a custom standard parent - P:- sage: selfpolicy = SelfParentPolicy(XYPairs, XYPair) sage: P = XYPairs(x=2, policy=selfpolicy) sage: pol = FacadeParentPolicy(XYPairs, P) sage: P2 = XYPairs(x=2, y=3, policy=pol) sage: el = P2.an_element() sage: el.parent() is P True sage: type(el) is P.element_class True - >>> from sage.all import * >>> selfpolicy = SelfParentPolicy(XYPairs, XYPair) >>> P = XYPairs(x=Integer(2), policy=selfpolicy) >>> pol = FacadeParentPolicy(XYPairs, P) >>> P2 = XYPairs(x=Integer(2), y=Integer(3), policy=pol) >>> el = P2.an_element() >>> el.parent() is P True >>> type(el) is P.element_class True - If - parentis itself a facade parent, then transitivity is correctly applied:- sage: P = XYPairs() sage: P2 = XYPairs(x=2) sage: P2.category() Category of facade finite enumerated sets sage: pol = FacadeParentPolicy(XYPairs, P) sage: P23 = XYPairs(x=2, y=3, policy=pol) sage: el = P2.an_element() sage: el.parent() is P True sage: type(el) is P.element_class True - >>> from sage.all import * >>> P = XYPairs() >>> P2 = XYPairs(x=Integer(2)) >>> P2.category() Category of facade finite enumerated sets >>> pol = FacadeParentPolicy(XYPairs, P) >>> P23 = XYPairs(x=Integer(2), y=Integer(3), policy=pol) >>> el = P2.an_element() >>> el.parent() is P True >>> type(el) is P.element_class True - element_constructor_attributes(constraints)[source]¶
- Return the element constructor attributes as per - SetFactoryPolicy.element_constructor_attributes().- INPUT: - constraints– a bunch of constraints
 
 
- class sage.structure.set_factories.ParentWithSetFactory(constraints, policy, category=None)[source]¶
- Bases: - Parent- Abstract class for parent belonging to a set factory. - INPUT: - constraints– set of constraints
- policy– the policy for element construction
- category– the category of the parent (default:- None)
 - Depending on the constraints and the policy, initialize the parent in a proper category to set up element construction. - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs, PairsX_ sage: P = PairsX_(3, XYPairs._default_policy) sage: P is XYPairs(3) True sage: P.category() Category of facade finite enumerated sets - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs, PairsX_ >>> P = PairsX_(Integer(3), XYPairs._default_policy) >>> P is XYPairs(Integer(3)) True >>> P.category() Category of facade finite enumerated sets - check_element(x, check)[source]¶
- Check that - xverifies the constraints of- self.- INPUT: - x– an instance of- self.element_class
- check– the level of checking to be performed (usually a boolean)
 - This method may assume that - xwas properly constructed by- selfor a possible super-set of- selffor which- selfis a facade. It should return nothing if- xverifies the constraints and raise a- ValueErrorexplaining which constraints- xfails otherwise.- The method should accept an extra parameter check specifying which level of check should be performed. It will only be called when - bool(check)evaluates to- True.- Todo - Should we always call check element and let it decide which check has to be performed ? - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: S = XYPairs() sage: el = S((2,3)) sage: S.check_element(el, True) sage: XYPairs(x=2).check_element(el, True) sage: XYPairs(x=3).check_element(el, True) Traceback (most recent call last): ... ValueError: Wrong first coordinate sage: XYPairs(y=4).check_element(el, True) Traceback (most recent call last): ... ValueError: Wrong second coordinate - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> S = XYPairs() >>> el = S((Integer(2),Integer(3))) >>> S.check_element(el, True) >>> XYPairs(x=Integer(2)).check_element(el, True) >>> XYPairs(x=Integer(3)).check_element(el, True) Traceback (most recent call last): ... ValueError: Wrong first coordinate >>> XYPairs(y=Integer(4)).check_element(el, True) Traceback (most recent call last): ... ValueError: Wrong second coordinate 
 - constraints()[source]¶
- Return the constraints defining - self.- Note - Currently there is no specification on how constraints are passed as arguments. - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: XYPairs().constraints() () sage: XYPairs(x=3).constraints() (3, None) sage: XYPairs(y=2).constraints() (None, 2) - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> XYPairs().constraints() () >>> XYPairs(x=Integer(3)).constraints() (3, None) >>> XYPairs(y=Integer(2)).constraints() (None, 2) 
 - facade_policy()[source]¶
- Return the policy for parent facade for - self.- EXAMPLES: - sage: from sage.structure.set_factories import SelfParentPolicy sage: from sage.structure.set_factories_example import XYPairs, XYPair - >>> from sage.all import * >>> from sage.structure.set_factories import SelfParentPolicy >>> from sage.structure.set_factories_example import XYPairs, XYPair - We create a custom standard parent - P:- sage: selfpolicy = SelfParentPolicy(XYPairs, XYPair) sage: P = XYPairs(x=2, policy=selfpolicy) sage: P.facade_policy() Set factory policy for facade parent {(2, b) | b in range(5)} - >>> from sage.all import * >>> selfpolicy = SelfParentPolicy(XYPairs, XYPair) >>> P = XYPairs(x=Integer(2), policy=selfpolicy) >>> P.facade_policy() Set factory policy for facade parent {(2, b) | b in range(5)} - Now passing - P.facade_policy()creates parent which are facade for- P:- sage: P3 = XYPairs(x=2, y=3, policy=P.facade_policy()) sage: P3.facade_for() == (P,) True sage: el = P3.an_element() sage: el.parent() is P True - >>> from sage.all import * >>> P3 = XYPairs(x=Integer(2), y=Integer(3), policy=P.facade_policy()) >>> P3.facade_for() == (P,) True >>> el = P3.an_element() >>> el.parent() is P True 
 - factory()[source]¶
- Return the factory which built - self.- EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: XYPairs().factory() is XYPairs True sage: XYPairs(x=3).factory() is XYPairs True - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> XYPairs().factory() is XYPairs True >>> XYPairs(x=Integer(3)).factory() is XYPairs True 
 - policy()[source]¶
- Return the policy used when - selfwas created.- EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: XYPairs().policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] sage: XYPairs(x=3).policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> XYPairs().policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] >>> XYPairs(x=Integer(3)).policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] 
 - subset(*args, **options)[source]¶
- Return a subset of - selfby adding more constraints.- Note - Currently there is no specification on how constraints are passed as arguments. - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: S = XYPairs() sage: S3 = S.subset(x=3) sage: S3.list() [(3, 0), (3, 1), (3, 2), (3, 3), (3, 4)] - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> S = XYPairs() >>> S3 = S.subset(x=Integer(3)) >>> S3.list() [(3, 0), (3, 1), (3, 2), (3, 3), (3, 4)] 
 
- class sage.structure.set_factories.SelfParentPolicy(factory, Element)[source]¶
- Bases: - SetFactoryPolicy- Policy where each parent is a standard parent. - INPUT: - factory– an instance of- SetFactory
- Element– a subclass of- Element
 - Given a factory - Fand a class- E, returns a policy for parent- Pcreating elements in class- Eand parent- Pitself.- EXAMPLES: - sage: from sage.structure.set_factories import SelfParentPolicy sage: from sage.structure.set_factories_example import XYPairs, XYPair, Pairs_Y sage: pol = SelfParentPolicy(XYPairs, XYPair) sage: S = Pairs_Y(3, pol) sage: el = S.an_element() sage: el.parent() is S True sage: class Foo(XYPair): pass sage: pol = SelfParentPolicy(XYPairs, Foo) sage: S = Pairs_Y(3, pol) sage: el = S.an_element() sage: isinstance(el, Foo) True - >>> from sage.all import * >>> from sage.structure.set_factories import SelfParentPolicy >>> from sage.structure.set_factories_example import XYPairs, XYPair, Pairs_Y >>> pol = SelfParentPolicy(XYPairs, XYPair) >>> S = Pairs_Y(Integer(3), pol) >>> el = S.an_element() >>> el.parent() is S True >>> class Foo(XYPair): pass >>> pol = SelfParentPolicy(XYPairs, Foo) >>> S = Pairs_Y(Integer(3), pol) >>> el = S.an_element() >>> isinstance(el, Foo) True - element_constructor_attributes(constraints)[source]¶
- Return the element constructor attributes as per - SetFactoryPolicy.element_constructor_attributes()- INPUT: - constraints– a bunch of constraints
 
 
- class sage.structure.set_factories.SetFactory[source]¶
- Bases: - UniqueRepresentation,- SageObject- This class is currently just a stub that we will be using to add more structures on factories. - add_constraints(cons, *args, **opts)[source]¶
- Add constraints to the set of constraints \(cons\). - Should return a set of constraints. - Note - Currently there is no specification on how constraints are passed as arguments. - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs sage: XYPairs.add_constraints((3,),((None, 2), {})) (3, 2) sage: XYPairs.add_constraints((3,),((None, None), {'y': 2})) (3, 2) - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs >>> XYPairs.add_constraints((Integer(3),),((None, Integer(2)), {})) (3, 2) >>> XYPairs.add_constraints((Integer(3),),((None, None), {'y': Integer(2)})) (3, 2) 
 
- class sage.structure.set_factories.SetFactoryPolicy(factory)[source]¶
- Bases: - UniqueRepresentation,- SageObject- Abstract base class for policies. - A policy is a device which is passed to a parent inheriting from - ParentWithSetFactoryin order to set-up the element construction framework.- INPUT: - factory– a- SetFactory
 - Warning - This class is a base class for policies, one should not try to create instances. - element_constructor_attributes(constraints)[source]¶
- Element constructor attributes. - INPUT: - constraints– a bunch of constraints
 - Should return the attributes that are prerequisite for element construction. This is coordinated with - ParentWithSetFactory._element_constructor_(). Currently two standard attributes are provided in- facade_element_constructor_attributes()and- self_element_constructor_attributes(). You should return the one needed depending on the given constraints.- EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs, XYPair sage: pol = XYPairs._default_policy sage: pol.element_constructor_attributes(()) {'Element': <class 'sage.structure.set_factories_example.XYPair'>, '_parent_for': 'self'} sage: pol.element_constructor_attributes((1)) {'_facade_for': AllPairs, '_parent_for': AllPairs, 'element_class': <class 'sage.structure.set_factories_example.AllPairs_with_category.element_class'>} - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs, XYPair >>> pol = XYPairs._default_policy >>> pol.element_constructor_attributes(()) {'Element': <class 'sage.structure.set_factories_example.XYPair'>, '_parent_for': 'self'} >>> pol.element_constructor_attributes((Integer(1))) {'_facade_for': AllPairs, '_parent_for': AllPairs, 'element_class': <class 'sage.structure.set_factories_example.AllPairs_with_category.element_class'>} 
 - facade_element_constructor_attributes(parent)[source]¶
- Element Constructor Attributes for facade parent. - The list of attributes which must be set during the init of a facade parent with factory. - INPUT: - parent– the actual parent for the elements
 - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs, XYPair sage: pol = XYPairs._default_policy sage: pol.facade_element_constructor_attributes(XYPairs()) {'_facade_for': AllPairs, '_parent_for': AllPairs, 'element_class': <class 'sage.structure.set_factories_example.AllPairs_with_category.element_class'>} - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs, XYPair >>> pol = XYPairs._default_policy >>> pol.facade_element_constructor_attributes(XYPairs()) {'_facade_for': AllPairs, '_parent_for': AllPairs, 'element_class': <class 'sage.structure.set_factories_example.AllPairs_with_category.element_class'>} 
 - factory()[source]¶
- Return the factory for - self.- EXAMPLES: - sage: from sage.structure.set_factories import SetFactoryPolicy, SelfParentPolicy sage: from sage.structure.set_factories_example import XYPairs, XYPair sage: XYPairs._default_policy.factory() Factory for XY pairs sage: XYPairs._default_policy.factory() is XYPairs True - >>> from sage.all import * >>> from sage.structure.set_factories import SetFactoryPolicy, SelfParentPolicy >>> from sage.structure.set_factories_example import XYPairs, XYPair >>> XYPairs._default_policy.factory() Factory for XY pairs >>> XYPairs._default_policy.factory() is XYPairs True 
 - self_element_constructor_attributes(Element)[source]¶
- Element Constructor Attributes for non facade parent. - The list of attributes which must be set during the init of a non facade parent with factory. - INPUT: - Element– the class used for the elements
 - EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs, XYPair sage: pol = XYPairs._default_policy sage: pol.self_element_constructor_attributes(XYPair) {'Element': <class 'sage.structure.set_factories_example.XYPair'>, '_parent_for': 'self'} - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs, XYPair >>> pol = XYPairs._default_policy >>> pol.self_element_constructor_attributes(XYPair) {'Element': <class 'sage.structure.set_factories_example.XYPair'>, '_parent_for': 'self'} 
 
- class sage.structure.set_factories.TopMostParentPolicy(factory, top_constraints, Element)[source]¶
- Bases: - SetFactoryPolicy- Policy where the parent of the elements is the topmost parent. - INPUT: - factory– an instance of- SetFactory
- top_constraints– the empty set of constraints
- Element– a subclass of- Element
 - Given a factory - Fand a class- E, returns a policy for parent- Pcreating element in class- Eand parent- factory(*top_constraints, policy).- EXAMPLES: - sage: from sage.structure.set_factories_example import XYPairs, XYPair sage: P = XYPairs(); P.policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] - >>> from sage.all import * >>> from sage.structure.set_factories_example import XYPairs, XYPair >>> P = XYPairs(); P.policy() Set factory policy for <class 'sage.structure.set_factories_example.XYPair'> with parent AllPairs[=Factory for XY pairs(())] - element_constructor_attributes(constraints)[source]¶
- Return the element constructor attributes as per - SetFactoryPolicy.element_constructor_attributes().- INPUT: - constraints– a bunch of constraints