# FiniteSetAggregate SΒΆ

aggcat.spad line 595 [edit on github]

S: SetCategory

A finite-set aggregate models the notion of a finite set, that is, a collection of elements characterized by membership, but not by order or multiplicity. See Set for an example.

- #: % -> NonNegativeInteger
from Aggregate

- <=: (%, %) -> Boolean
from PartialOrder

- <: (%, %) -> Boolean
from PartialOrder

- >=: (%, %) -> Boolean
from PartialOrder

- >: (%, %) -> Boolean
from PartialOrder

- any?: (S -> Boolean, %) -> Boolean
from HomogeneousAggregate S

- cardinality: % -> NonNegativeInteger
`cardinality(u)`

returns the number of elements of`u`

. Note:`cardinality(u) = \#u`

.

- coerce: % -> OutputForm
from CoercibleTo OutputForm

- complement: % -> % if S has Finite
`complement(u)`

returns the complement of the set`u`

, i.e. the set of all values not in`u`

.

- construct: List S -> %
from Collection S

- convert: % -> InputForm if S has ConvertibleTo InputForm
from ConvertibleTo InputForm

- count: (S -> Boolean, %) -> NonNegativeInteger
from HomogeneousAggregate S

- count: (S, %) -> NonNegativeInteger
from HomogeneousAggregate S

- dictionary: () -> %
from DictionaryOperations S

- dictionary: List S -> %
from DictionaryOperations S

- difference: (%, %) -> %
from SetAggregate S

- difference: (%, S) -> %
from SetAggregate S

- eval: (%, Equation S) -> % if S has Evalable S
from Evalable S

- eval: (%, List Equation S) -> % if S has Evalable S
from Evalable S

- eval: (%, List S, List S) -> % if S has Evalable S
from InnerEvalable(S, S)

- eval: (%, S, S) -> % if S has Evalable S
from InnerEvalable(S, S)

- every?: (S -> Boolean, %) -> Boolean
from HomogeneousAggregate S

- extract!: % -> S
from BagAggregate S

- find: (S -> Boolean, %) -> Union(S, failed)
from Collection S

- hash: % -> SingleInteger if S has Finite
from Hashable

- hashUpdate!: (HashState, %) -> HashState if S has Finite
from Hashable

- index: PositiveInteger -> % if S has Finite
from Finite

- insert!: (S, %) -> %
from BagAggregate S

- inspect: % -> S
from BagAggregate S

- intersect: (%, %) -> %
from SetAggregate S

- latex: % -> String
from SetCategory

- less?: (%, NonNegativeInteger) -> Boolean
from Aggregate

- lookup: % -> PositiveInteger if S has Finite
from Finite

- map!: (S -> S, %) -> %
from HomogeneousAggregate S

- map: (S -> S, %) -> %
from HomogeneousAggregate S

- max: % -> S if S has OrderedSet
from HomogeneousAggregate S

- max: ((S, S) -> Boolean, %) -> S
from HomogeneousAggregate S

- member?: (S, %) -> Boolean
from HomogeneousAggregate S

- members: % -> List S
from HomogeneousAggregate S

- min: % -> S if S has OrderedSet
from HomogeneousAggregate S

- more?: (%, NonNegativeInteger) -> Boolean
from Aggregate

- parts: % -> List S
from HomogeneousAggregate S

- reduce: ((S, S) -> S, %) -> S
from Collection S

- reduce: ((S, S) -> S, %, S) -> S
from Collection S

- reduce: ((S, S) -> S, %, S, S) -> S
from Collection S

- remove!: (S -> Boolean, %) -> %
from DictionaryOperations S

- remove!: (S, %) -> %
from DictionaryOperations S

- remove: (S -> Boolean, %) -> %
from Collection S

- remove: (S, %) -> %
from Collection S

- removeDuplicates: % -> %
from Collection S

- select!: (S -> Boolean, %) -> %
from DictionaryOperations S

- select: (S -> Boolean, %) -> %
from Collection S

- set: () -> %
from SetAggregate S

- set: List S -> %
from SetAggregate S

- size?: (%, NonNegativeInteger) -> Boolean
from Aggregate

- size: () -> NonNegativeInteger if S has Finite
from Finite

- smaller?: (%, %) -> Boolean if S has Comparable
from Comparable

- subset?: (%, %) -> Boolean
from SetAggregate S

- symmetricDifference: (%, %) -> %
from SetAggregate S

- union: (%, %) -> %
from SetAggregate S

- union: (%, S) -> %
from SetAggregate S

- union: (S, %) -> %
from SetAggregate S

- universe: () -> % if S has Finite
`universe()`

$`D`

returns the universal set for finite set aggregate`D`

.

Comparable if S has Comparable

ConvertibleTo InputForm if S has ConvertibleTo InputForm

Evalable S if S has Evalable S

InnerEvalable(S, S) if S has Evalable S