Coverage for local/lib/python2.7/site-packages/sage/categories/examples/infinite_enumerated_sets.py : 46%

""" 

Examples of infinite 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.categories.infinite_enumerated_sets import InfiniteEnumeratedSets 

from sage.structure.unique_representation import UniqueRepresentation 

from sage.rings.integer import Integer 

class NonNegativeIntegers(UniqueRepresentation, Parent): 

r""" 

An example of infinite enumerated set: the non negative integers 

This class provides a minimal implementation of an infinite enumerated set. 

EXAMPLES:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: NN 

An example of an infinite enumerated set: the non negative integers 

sage: NN.cardinality() 

+Infinity 

sage: NN.list() 

Traceback (most recent call last): 

... 

NotImplementedError: cannot list an infinite set 

sage: NN.element_class 

<type 'sage.rings.integer.Integer'> 

sage: it = iter(NN) 

sage: [next(it), next(it), next(it), next(it), next(it)] 

[0, 1, 2, 3, 4] 

sage: x = next(it); type(x) 

<type 'sage.rings.integer.Integer'> 

sage: x.parent() 

Integer Ring 

sage: x+3 

8 

sage: NN(15) 

15 

sage: NN.first() 

0 

This checks that the different methods of `NN` return consistent 

results:: 

sage: TestSuite(NN).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: NN = InfiniteEnumeratedSets().example() 

sage: NN 

An example of an infinite enumerated set: the non negative integers 

sage: NN.category() 

Category of infinite enumerated sets 

sage: TestSuite(NN).run() 

""" 

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

def _repr_(self): 

""" 

TESTS:: 

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

An example of an infinite enumerated set: the non negative integers 

""" 

return "An example of an infinite enumerated set: the non negative integers" 

def __contains__(self, elt): 

""" 

EXAMPLES:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: 1 in NN 

True 

sage: -1 in NN 

False 

""" 

return Integer(elt) >= Integer(0) 

def __iter__(self): 

""" 

EXAMPLES:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: g = iter(NN) 

sage: next(g), next(g), next(g), next(g) 

(0, 1, 2, 3) 

""" 

i = Integer(0) 

while True: 

yield self._element_constructor_(i) 

i += 1 

def __call__(self, elt): 

""" 

EXAMPLES:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: NN(3) # indirect doctest 

3 

sage: NN(3).parent() 

Integer Ring 

sage: NN(-1) 

Traceback (most recent call last): 

ValueError: Value -1 is not a non negative integer. 

""" 

if elt in self: 

return self._element_constructor_(elt) 

else: 

raise ValueError("Value %s is not a non negative integer."%(elt)) 

def an_element(self): 

""" 

EXAMPLES:: 

sage: InfiniteEnumeratedSets().example().an_element() 

42 

""" 

return self._element_constructor_(Integer(42)) 

def next(self, o): 

""" 

EXAMPLES:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: NN.next(3) 

4 

""" 

return self._element_constructor_(o+1) 

def _element_constructor_(self, i): 

""" 

The default implementation of _element_constructor_ assumes 

that the constructor of the element class takes the parent as 

parameter. This is not the case for ``Integer``, so we need to 

provide an implementation. 

TESTS:: 

sage: NN = InfiniteEnumeratedSets().example() 

sage: x = NN(42); x 

42 

sage: type(x) 

<type 'sage.rings.integer.Integer'> 

sage: x.parent() 

Integer Ring 

""" 

return self.element_class(i) 

Element = Integer 

Example = NonNegativeIntegers