# An example of set factory#

The goal of this module is to exemplify the use of set factories. Note that the code is intentionally kept minimal; many things and in particular several iterators could be written in a more efficient way.

See also

set_factories for an introduction to set factories, their specifications, and examples of their use and implementation based on this module.

We describe here a factory used to construct the set $$S$$ of couples $$(x,y)$$ with $$x$$ and $$y$$ in $$I:=\{0,1,2,3,4\}$$, together with the following subsets, where $$(a, b)\in S$$

\begin{align}\begin{aligned}S_a := \{(x,y) \in S \mid x = a\},\\S^b := \{(x,y) \in S \mid y = b\},\\S_a^b := \{(x,y) \in S \mid x = a, y = b\}.\end{aligned}\end{align}
class sage.structure.set_factories_example.AllPairs(policy)[source]#

This parent shows how one can use set factories together with DisjointUnionEnumeratedSets.

It is constructed as the disjoint union (DisjointUnionEnumeratedSets) of Pairs_Y parents:

$S := \bigcup_{i = 0,1,..., 4} S^y$

Warning

When writing a parent P as a disjoint union of a family of parents P_i, the parents P_i must be constructed as facade parents for P. As a consequence, it should be passed P.facade_policy() as policy argument. See the source code of pairs_y() for an example.

check_element(el, check)[source]#
pairs_y(letter)[source]#

Construct the parent for the disjoint union

Construct a parent in Pairs_Y as a facade parent for self.

This is an internal function which should be hidden from the user (typically under the name _pairs_y. We put it here for documentation.

class sage.structure.set_factories_example.PairsX_(x, policy)[source]#

The set of pairs $$(x, 0), (x, 1), ..., (x, 4)$$.

an_element()[source]#
check_element(el, check)[source]#
class sage.structure.set_factories_example.Pairs_Y(y, policy)[source]#

The set of pairs $$(0, y), (1, y), ..., (4, y)$$.

It is constructed as the disjoint union (DisjointUnionEnumeratedSets) of SingletonPair parents:

$S^y := \bigcup_{i = 0,1,..., 4} S_i^y$
an_element()[source]#
check_element(el, check)[source]#
single_pair(letter)[source]#

Construct the singleton pair parent

Construct a singleton pair for (self.y, letter) as a facade parent for self.

class sage.structure.set_factories_example.SingletonPair(x, y, policy)[source]#
check_element(el, check)[source]#
class sage.structure.set_factories_example.XYPair(parent, value, check=True)[source]#

Bases: ElementWrapper

A class for Elements $$(x,y)$$ with $$x$$ and $$y$$ in $$\{0,1,2,3,4\}$$.

EXAMPLES:

sage: from sage.structure.set_factories_example import XYPair
sage: p = XYPair(Parent(), (0,1)); p
(0, 1)
sage: p = XYPair(Parent(), (0,8))
Traceback (most recent call last):
...
ValueError: numbers must be in range(5)

>>> from sage.all import *
>>> from sage.structure.set_factories_example import XYPair
>>> p = XYPair(Parent(), (Integer(0),Integer(1))); p
(0, 1)
>>> p = XYPair(Parent(), (Integer(0),Integer(8)))
Traceback (most recent call last):
...
ValueError: numbers must be in range(5)

sage.structure.set_factories_example.XYPairs(x=None, y=None, policy=None)[source]#

Construct the subset from constraints.

Consider the set $$S$$ of couples $$(x,y)$$ with $$x$$ and $$y$$ in $$I:=\{0,1,2,3,4\}$$. Returns the subsets of element of $$S$$ satisfying some constraints.

INPUT:

• x=a – where a is an integer (default to None).

• y=b – where b is an integer (default to None).

• policy – the policy passed to the created set.

EXAMPLES:

Let us first create the set factory:

sage: from sage.structure.set_factories_example import XYPairsFactory
sage: XYPairs = XYPairsFactory()

>>> from sage.all import *
>>> from sage.structure.set_factories_example import XYPairsFactory
>>> XYPairs = XYPairsFactory()


One can then use the set factory to construct a set:

sage: P = XYPairs(); P.list()
[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (0, 2), (1, 2), (2, 2), (3, 2), (4, 2), (0, 3), (1, 3), (2, 3), (3, 3), (4, 3), (0, 4), (1, 4), (2, 4), (3, 4), (4, 4)]

>>> from sage.all import *
>>> P = XYPairs(); P.list()
[(0, 0), (1, 0), (2, 0), (3, 0), (4, 0), (0, 1), (1, 1), (2, 1), (3, 1), (4, 1), (0, 2), (1, 2), (2, 2), (3, 2), (4, 2), (0, 3), (1, 3), (2, 3), (3, 3), (4, 3), (0, 4), (1, 4), (2, 4), (3, 4), (4, 4)]


Note

This function is actually the __call__ method of XYPairsFactory.

class sage.structure.set_factories_example.XYPairsFactory[source]#

Bases: SetFactory

An example of set factory, for sets of pairs of integers.

See also

set_factories for an introduction to set factories.

add_constraints(cons, args_opts)[source]#

Add constraints to the set cons as per SetFactory.add_constraints.

This is a crude implementation for the sake of the demonstration which should not be taken as an example.

EXAMPLES:

sage: from sage.structure.set_factories_example import XYPairs
sage: XYPairs.add_constraints((3,None), ((2,), {}))
Traceback (most recent call last):
...
ValueError: Duplicate value for constraints 'x': was 3 now 2
sage: XYPairs.add_constraints((), ((2,), {}))
(2, None)
sage: XYPairs.add_constraints((), ((2,), {'y':3}))
(2, 3)

>>> from sage.all import *
>>> from sage.structure.set_factories_example import XYPairs
>>> XYPairs.add_constraints((Integer(3),None), ((Integer(2),), {}))
Traceback (most recent call last):
...
ValueError: Duplicate value for constraints 'x': was 3 now 2
>>> XYPairs.add_constraints((), ((Integer(2),), {}))
(2, None)
>>> XYPairs.add_constraints((), ((Integer(2),), {'y':Integer(3)}))
(2, 3)