Coverage for local/lib/python2.7/site-packages/sage/sets/positive_integers.py : 33%

""" 

Positive Integers 

""" 

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

# Copyright (C) 2010 Nicolas Borie <nicolas.borie@math.u-psud.fr> 

# 

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

# http://www.gnu.org/licenses/ 

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

from sage.sets.integer_range import IntegerRangeInfinite 

from sage.rings.integer import Integer 

class PositiveIntegers(IntegerRangeInfinite): 

r""" 

The enumerated set of positive integers. To fix the ideas, 

we mean `\{1, 2, 3, 4, 5, \dots \}`. 

This class implements the set of positive integers, as an 

enumerated set (see :class:`InfiniteEnumeratedSets 

<sage.categories.infinite_enumerated_sets.InfiniteEnumeratedSets>`). 

This set is an integer range set. The construction is 

therefore done by IntegerRange (see :class:`IntegerRange 

<sage.sets.integer_range.IntegerRange>`). 

EXAMPLES:: 

sage: PP = PositiveIntegers() 

sage: PP 

Positive integers 

sage: PP.cardinality() 

+Infinity 

sage: TestSuite(PP).run() 

sage: PP.list() 

Traceback (most recent call last): 

... 

NotImplementedError: cannot list an infinite set 

sage: it = iter(PP) 

sage: (next(it), next(it), next(it), next(it), next(it)) 

(1, 2, 3, 4, 5) 

sage: PP.first() 

1 

TESTS:: 

sage: TestSuite(PositiveIntegers()).run() 

""" 

def __init__(self): 

r""" 

EXAMPLES:: 

sage: PP = PositiveIntegers() 

sage: PP.category() 

Category of facade infinite enumerated sets 

""" 

IntegerRangeInfinite.__init__(self, Integer(1), Integer(1)) 

def _repr_(self): 

r""" 

EXAMPLES:: 

sage: PositiveIntegers() 

Positive integers 

""" 

return "Positive integers" 

def an_element(self): 

r""" 

Returns an element of ``self``. 

EXAMPLES:: 

sage: PositiveIntegers().an_element() 

42 

""" 

return Integer(42)