Examples of infinite enumerated sets#

sage.categories.examples.infinite_enumerated_sets.Example[source]#: alias of NonNegativeIntegers

class sage.categories.examples.infinite_enumerated_sets.NonNegativeIntegers[source]#

Bases: UniqueRepresentation, Parent

An example of infinite enumerated set: the non negative integers

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

EXAMPLES:

Sage

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
<class '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)
<class 'sage.rings.integer.Integer'>
sage: x.parent()
Integer Ring
sage: x+3
8
sage: NN(15)
15
sage: NN.first()
0

Python

>>> from sage.all import *
>>> NN = InfiniteEnumeratedSets().example()
>>> NN
An example of an infinite enumerated set: the non negative integers
>>> NN.cardinality()
+Infinity
>>> NN.list()
Traceback (most recent call last):
...
NotImplementedError: cannot list an infinite set
>>> NN.element_class
<class 'sage.rings.integer.Integer'>
>>> it = iter(NN)
>>> [next(it), next(it), next(it), next(it), next(it)]
[0, 1, 2, 3, 4]
>>> x = next(it); type(x)
<class 'sage.rings.integer.Integer'>
>>> x.parent()
Integer Ring
>>> x+Integer(3)
8
>>> NN(Integer(15))
15
>>> NN.first()
0

This checks that the different methods of \(NN\) return consistent results:

Sage

sage: TestSuite(NN).run(verbose = True)
running ._test_an_element() . . . pass
running ._test_cardinality() . . . pass
running ._test_category() . . . pass
running ._test_construction() . . . 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

Python

>>> from sage.all import *
>>> TestSuite(NN).run(verbose = True)
running ._test_an_element() . . . pass
running ._test_cardinality() . . . pass
running ._test_category() . . . pass
running ._test_construction() . . . 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

Element[source]#: alias of Integer

an_element()[source]#

EXAMPLES:

Sage

sage: InfiniteEnumeratedSets().example().an_element()
42

Python

>>> from sage.all import *
>>> InfiniteEnumeratedSets().example().an_element()
42

next(o)[source]#

EXAMPLES:

Sage

sage: NN = InfiniteEnumeratedSets().example()
sage: NN.next(3)
4

Python

>>> from sage.all import *
>>> NN = InfiniteEnumeratedSets().example()
>>> NN.next(Integer(3))
4