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

""" 

Examples of posets 

""" 

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

# Copyright (C) 2011 Nicolas M. Thiery <nthiery at users.sf.net> 

# 

# 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.all import Posets 

from sage.structure.element_wrapper import ElementWrapper 

from sage.sets.set import Set, Set_object_enumerated 

from sage.sets.positive_integers import PositiveIntegers 

class FiniteSetsOrderedByInclusion(UniqueRepresentation, Parent): 

r""" 

An example of a poset: finite sets ordered by inclusion 

This class provides a minimal implementation of a poset 

EXAMPLES:: 

sage: P = Posets().example(); P 

An example of a poset: sets ordered by inclusion 

We conclude by running systematic tests on this poset:: 

sage: TestSuite(P).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_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_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_pickling() . . . pass 

running ._test_some_elements() . . . pass 

""" 

def __init__(self): 

r""" 

EXAMPLES:: 

sage: P = Posets().example(); P 

An example of a poset: sets ordered by inclusion 

sage: P.category() 

Category of posets 

sage: type(P) 

<class 'sage.categories.examples.posets.FiniteSetsOrderedByInclusion_with_category'> 

sage: TestSuite(P).run() 

""" 

Parent.__init__(self, category = Posets()) 

def _repr_(self): 

r""" 

TESTS:: 

sage: S = Posets().example() 

sage: S._repr_() 

'An example of a poset: sets ordered by inclusion' 

""" 

return "An example of a poset: sets ordered by inclusion" 

def le(self, x, y): 

r""" 

Returns whether `x` is a subset of `y` 

EXAMPLES:: 

sage: P = Posets().example() 

sage: P.le( P(Set([1,3])), P(Set([1,2,3])) ) 

True 

sage: P.le( P(Set([1,3])), P(Set([1,3])) ) 

True 

sage: P.le( P(Set([1,2])), P(Set([1,3])) ) 

False 

""" 

return x.value.issubset(y.value) 

def an_element(self): 

r""" 

Returns an element of this poset 

EXAMPLES:: 

sage: B = Posets().example() 

sage: B.an_element() 

{1, 4, 6} 

""" 

return self(Set([1,4,6])) 

class Element(ElementWrapper): 

wrapped_class = Set_object_enumerated 

class PositiveIntegersOrderedByDivisibilityFacade(UniqueRepresentation, Parent): 

r""" 

An example of a facade poset: the positive integers ordered by divisibility 

This class provides a minimal implementation of a facade poset 

EXAMPLES:: 

sage: P = Posets().example("facade"); P 

An example of a facade poset: the positive integers ordered by divisibility 

sage: P(5) 

5 

sage: P(0) 

Traceback (most recent call last): 

... 

ValueError: Can't coerce `0` in any parent `An example of a facade poset: the positive integers ordered by divisibility` is a facade for 

sage: 3 in P 

True 

sage: 0 in P 

False 

""" 

element_class = type(Set([])) 

def __init__(self): 

r""" 

EXAMPLES:: 

sage: P = Posets().example("facade"); P 

An example of a facade poset: the positive integers ordered by divisibility 

sage: P.category() 

Category of facade posets 

sage: type(P) 

<class 'sage.categories.examples.posets.PositiveIntegersOrderedByDivisibilityFacade_with_category'> 

sage: TestSuite(P).run() 

""" 

Parent.__init__(self, facade = (PositiveIntegers(),), category = Posets()) 

def _repr_(self): 

r""" 

TESTS:: 

sage: S = Posets().example("facade") 

sage: S._repr_() 

'An example of a facade poset: the positive integers ordered by divisibility' 

""" 

return "An example of a facade poset: the positive integers ordered by divisibility" 

def le(self, x, y): 

r""" 

Returns whether `x` is divisible by `y` 

EXAMPLES:: 

sage: P = Posets().example("facade") 

sage: P.le(3, 6) 

True 

sage: P.le(3, 3) 

True 

sage: P.le(3, 7) 

False 

""" 

return x.divides(y)