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

r""" 

Example of facade set 

""" 

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

# Copyright (C) 2010 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.categories.sets_cat import Sets 

from sage.categories.monoids import Monoids 

from sage.structure.parent import Parent 

from sage.structure.unique_representation import UniqueRepresentation 

from sage.rings.integer_ring import ZZ 

from sage.rings.infinity import infinity 

from sage.sets.finite_enumerated_set import FiniteEnumeratedSet 

class PositiveIntegerMonoid(UniqueRepresentation, Parent): 

r""" 

An example of a facade parent: the positive integers viewed as a 

multiplicative monoid 

This class illustrates a minimal implementation of a facade parent 

which models a subset of a set. 

EXAMPLES:: 

sage: S = Sets().Facade().example(); S 

An example of facade set: the monoid of positive integers 

TESTS:: 

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

running ._test_an_element() . . . pass 

running ._test_associativity() . . . 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_eq() . . . pass 

running ._test_new() . . . pass 

running ._test_not_implemented_methods() . . . pass 

running ._test_one() . . . pass 

running ._test_pickling() . . . pass 

running ._test_prod() . . . pass 

running ._test_some_elements() . . . pass 

""" 

def __init__(self): 

r""" 

EXAMPLES:: 

sage: from sage.categories.examples.facade_sets import PositiveIntegerMonoid 

sage: S = PositiveIntegerMonoid(); S 

An example of facade set: the monoid of positive integers 

TESTS:: 

sage: TestSuite(S).run() 

""" 

Parent.__init__(self, facade = ZZ, category = Monoids()) 

def _repr_(self): 

r""" 

EXAMPLES:: 

sage: S = Sets().Facade().example() # indirect doctest 

""" 

return "An example of facade set: the monoid of positive integers" 

def _element_constructor_(self, object): 

r""" 

Construction of elements 

Since ``self`` is a strict subset of the parent it is a facade 

for, it is mandatory to override this method. This method 

indirectly influences membership testing (see 

:meth:`Parent.__contains__`). 

EXAMPLES:: 

sage: S = Sets().Facade().example(); S 

An example of facade set: the monoid of positive integers 

sage: S(1) 

1 

sage: S(int(1)) 

1 

sage: S(2/1) 

2 

sage: (parent(S(1)) == ZZ, parent(S(int(1))) == ZZ, parent(S(2/1))) 

(True, True, Integer Ring) 

sage: S(1), S(int(1)), S(2/1) 

(1, 1, 2) 

sage: 1 in S 

True 

sage: 2/1 in S, int(1) in S 

(True, True) 

sage: -1 in S, 1/2 in S 

(False, False) 

""" 

object = ZZ(object) 

if object > ZZ(0): 

return object 

else: 

raise ValueError("%s should be positive") 

class IntegersCompletion(UniqueRepresentation, Parent): 

r""" 

An example of a facade parent: the set of integers completed with 

`+-\infty` 

This class illustrates a minimal implementation of a facade parent 

that models the union of several other parents. 

EXAMPLES:: 

sage: S = Sets().Facade().example("union"); S 

An example of a facade set: the integers completed by +-infinity 

TESTS:: 

sage: TestSuite(S).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_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: from sage.categories.examples.facade_sets import IntegersCompletion 

sage: S = IntegersCompletion(); S 

An example of a facade set: the integers completed by +-infinity 

TESTS:: 

sage: TestSuite(S).run() 

""" 

# We can't use InfinityRing, because this ring contains 3 

# elements besides +-infinity. We can't use Set either for the 

# moment, because Set([1,2])(1) raises an error 

Parent.__init__(self, facade = (ZZ, FiniteEnumeratedSet([-infinity, +infinity])), category = Sets()) 

def _repr_(self): 

r""" 

EXAMPLES:: 

sage: S = Sets().Facade().example() # indirect doctest 

""" 

return "An example of a facade set: the integers completed by +-infinity"