Finite Enumerated Sets

class sage.sets.finite_enumerated_set.FiniteEnumeratedSet(elements)

Bases: UniqueRepresentation, Parent

A class for finite enumerated set.

Returns the finite enumerated set with elements in elements where element is any (finite) iterable object.

The main purpose is to provide a variant of list or tuple, which is a parent with an interface consistent with EnumeratedSets and has unique representation. The list of the elements is expanded in memory.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet([1, 2, 3])
sage: S
{1, 2, 3}
sage: S.list()
[1, 2, 3]
sage: S.cardinality()
3
sage: S.random_element()  # random
1
sage: S.first()
1
sage: S.category()
Category of facade finite enumerated sets
sage: TestSuite(S).run()

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet([Integer(1), Integer(2), Integer(3)])
>>> S
{1, 2, 3}
>>> S.list()
[1, 2, 3]
>>> S.cardinality()
3
>>> S.random_element()  # random
1
>>> S.first()
1
>>> S.category()
Category of facade finite enumerated sets
>>> TestSuite(S).run()

Note that being an enumerated set, the result depends on the order:

Sage

sage: S1 = FiniteEnumeratedSet((1, 2, 3))
sage: S1
{1, 2, 3}
sage: S1.list()
[1, 2, 3]
sage: S1 == S
True
sage: S2 = FiniteEnumeratedSet((2, 1, 3))
sage: S2 == S
False

Python

>>> from sage.all import *
>>> S1 = FiniteEnumeratedSet((Integer(1), Integer(2), Integer(3)))
>>> S1
{1, 2, 3}
>>> S1.list()
[1, 2, 3]
>>> S1 == S
True
>>> S2 = FiniteEnumeratedSet((Integer(2), Integer(1), Integer(3)))
>>> S2 == S
False

As an abuse, repeated entries in elements are allowed to model multisets:

Sage

sage: S1 = FiniteEnumeratedSet((1, 2, 1, 2, 2, 3))
sage: S1
{1, 2, 1, 2, 2, 3}

Python

>>> from sage.all import *
>>> S1 = FiniteEnumeratedSet((Integer(1), Integer(2), Integer(1), Integer(2), Integer(2), Integer(3)))
>>> S1
{1, 2, 1, 2, 2, 3}

Finally, the elements are not aware of their parent:

Sage

sage: S.first().parent()
Integer Ring

Python

>>> from sage.all import *
>>> S.first().parent()
Integer Ring

an_element()

cardinality()

first()

Return the first element of the enumeration or raise an EmptySetError if the set is empty.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet('abc')
sage: S.first()
'a'

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet('abc')
>>> S.first()
'a'

index(x)

Return the index of x in this finite enumerated set.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet(['a','b','c'])
sage: S.index('b')
1

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet(['a','b','c'])
>>> S.index('b')
1

is_parent_of(x)

last()

Return the last element of the iteration or raise an EmptySetError if the set is empty.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet([0,'a',1.23, 'd'])
sage: S.last()
'd'

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet([Integer(0),'a',RealNumber('1.23'), 'd'])
>>> S.last()
'd'

list()

random_element()

Return a random element.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet('abc')
sage: S.random_element()   # random
'b'

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet('abc')
>>> S.random_element()   # random
'b'

rank(x)

Return the index of x in this finite enumerated set.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet(['a','b','c'])
sage: S.index('b')
1

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet(['a','b','c'])
>>> S.index('b')
1

unrank(i)

Return the element at position i.

EXAMPLES:

Sage

sage: S = FiniteEnumeratedSet([1,'a',-51])
sage: S[0], S[1], S[2]
(1, 'a', -51)
sage: S[3]
Traceback (most recent call last):
...
IndexError: tuple index out of range
sage: S[-1], S[-2], S[-3]
(-51, 'a', 1)
sage: S[-4]
Traceback (most recent call last):
...
IndexError: list index out of range

Python

>>> from sage.all import *
>>> S = FiniteEnumeratedSet([Integer(1),'a',-Integer(51)])
>>> S[Integer(0)], S[Integer(1)], S[Integer(2)]
(1, 'a', -51)
>>> S[Integer(3)]
Traceback (most recent call last):
...
IndexError: tuple index out of range
>>> S[-Integer(1)], S[-Integer(2)], S[-Integer(3)]
(-51, 'a', 1)
>>> S[-Integer(4)]
Traceback (most recent call last):
...
IndexError: list index out of range