Coverage for local/lib/python2.7/site-packages/sage/categories/examples/finite_enumerated_sets.py : 100%

r""" 

Examples of finite enumerated sets 

""" 

#***************************************************************************** 

# Copyright (C) 2009 Florent Hivert <Florent.Hivert@univ-rouen.fr> 

# 

# Distributed under the terms of the GNU General Public License (GPL) 

# http://www.gnu.org/licenses/ 

#****************************************************************************** 

from sage.structure.parent import Parent 

from sage.structure.unique_representation import UniqueRepresentation 

from sage.categories.finite_enumerated_sets import FiniteEnumeratedSets 

from sage.rings.integer import Integer 

from sage.rings.integer_ring import IntegerRing 

from sage.functions.other import sqrt 

class Example(UniqueRepresentation, Parent): 

r""" 

An example of a finite enumerated set: `\{1,2,3\}` 

This class provides a minimal implementation of a finite enumerated set. 

See :class:`~sage.sets.finite_enumerated_set.FiniteEnumeratedSet` for a 

full featured implementation. 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().example() 

sage: C.cardinality() 

3 

sage: C.list() 

[1, 2, 3] 

sage: C.an_element() 

1 

This checks that the different methods of the enumerated set `C` 

return consistent results:: 

sage: TestSuite(C).run(verbose = True) 

running ._test_an_element() . . . pass 

running ._test_cardinality() . . . pass 

running ._test_category() . . . pass 

running ._test_elements() . . . 

Running the test suite of self.an_element() 

running ._test_category() . . . pass 

running ._test_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_nonzero_equal() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_pickling() . . . pass 

pass 

running ._test_elements_eq_reflexive() . . . pass 

running ._test_elements_eq_symmetric() . . . pass 

running ._test_elements_eq_transitive() . . . pass 

running ._test_elements_neq() . . . pass 

running ._test_enumerated_set_contains() . . . pass 

running ._test_enumerated_set_iter_cardinality() . . . pass 

running ._test_enumerated_set_iter_list() . . . pass 

running ._test_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_pickling() . . . pass 

running ._test_some_elements() . . . pass 

""" 

def __init__(self): 

""" 

TESTS:: 

sage: C = FiniteEnumeratedSets().example() 

sage: C 

An example of a finite enumerated set: {1,2,3} 

sage: C.category() 

Category of facade finite enumerated sets 

sage: TestSuite(C).run() 

""" 

self._set = [Integer(_) for _ in [1,2,3]] 

Parent.__init__(self, facade = IntegerRing(), category = FiniteEnumeratedSets()) 

def _repr_(self): 

""" 

TESTS:: 

sage: FiniteEnumeratedSets().example() # indirect doctest 

An example of a finite enumerated set: {1,2,3} 

""" 

return "An example of a finite enumerated set: {1,2,3}" 

def __contains__(self, o): 

""" 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().example() 

sage: 1 in C 

True 

sage: 0 in C 

False 

""" 

return o in self._set 

def __iter__(self): 

""" 

EXAMPLES:: 

sage: list(FiniteEnumeratedSets().example()) # indirect doctest 

[1, 2, 3] 

""" 

return iter(self._set) 

class IsomorphicObjectOfFiniteEnumeratedSet(UniqueRepresentation, Parent): 

def __init__(self, ambient = Example()): 

""" 

TESTS:: 

sage: C = FiniteEnumeratedSets().IsomorphicObjects().example() 

sage: C 

The image by some isomorphism of An example of a finite enumerated set: {1,2,3} 

sage: C.category() 

Category of facade isomorphic objects of finite enumerated sets 

sage: TestSuite(C).run() 

""" 

self._ambient = ambient 

Parent.__init__(self, facade = IntegerRing(), category = FiniteEnumeratedSets().IsomorphicObjects()) 

def ambient(self): 

""" 

Returns the ambient space for ``self``, as per 

:meth:`Sets.Subquotients.ParentMethods.ambient() 

<sage.categories.sets_cat.Sets.Subquotients.ParentMethods.ambient>`. 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C 

The image by some isomorphism of An example of a finite enumerated set: {1,2,3} 

sage: C.ambient() 

An example of a finite enumerated set: {1,2,3} 

""" 

return self._ambient 

def lift(self, x): 

""" 

INPUT: 

- ``x`` -- an element of ``self`` 

Lifts ``x`` to the ambient space for ``self``, as per 

:meth:`Sets.Subquotients.ParentMethods.lift() 

<sage.categories.sets_cat.Sets.Subquotients.ParentMethods.lift>`. 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C 

The image by some isomorphism of An example of a finite enumerated set: {1,2,3} 

sage: C.lift(9) 

3 

""" 

return sqrt(x) 

def retract(self, x): 

""" 

INPUT: 

- ``x`` -- an element of the ambient space for ``self`` 

Retracts ``x`` from the ambient space to ``self``, as per 

:meth:`Sets.Subquotients.ParentMethods.retract() 

<sage.categories.sets_cat.Sets.Subquotients.ParentMethods.retract>`. 

EXAMPLES:: 

sage: C = FiniteEnumeratedSets().IsomorphicObjects().example(); C 

The image by some isomorphism of An example of a finite enumerated set: {1,2,3} 

sage: C.retract(3) 

9 

""" 

return x ** 2 

def __contains__(self, x): 

""" 

Membership testing by checking whether the preimage by the 

bijection is in the ambient space. 

EXAMPLES:: 

sage: A = FiniteEnumeratedSets().IsomorphicObjects().example(); A 

The image by some isomorphism of An example of a finite enumerated set: {1,2,3} 

sage: list(A) 

[1, 4, 9] 

sage: 4 in A 

True 

sage: 3 in A 

False 

sage: None in A 

False 

TODO: devise a robust implementation, and move it up to 

``FiniteEnumeratedSets.IsomorphicObjects``. 

""" 

try: 

return self.lift(x) in self.ambient() 

except Exception: 

return False