# Multiset SΒΆ

- S: SetCategory

A multiset is a set with multiplicities.

- <: (%, %) -> Boolean
- from PartialOrder
- <=: (%, %) -> Boolean
- from PartialOrder
- =: (%, %) -> Boolean
- from BasicType
- >: (%, %) -> Boolean
- from PartialOrder
- >=: (%, %) -> Boolean
- from PartialOrder
- ~=: (%, %) -> Boolean
- from BasicType
- brace: () -> %
- from SetAggregate S
- brace: List S -> %
- from SetAggregate S
- coerce: % -> OutputForm
- from CoercibleTo OutputForm
- construct: List S -> %
- from Collection S
- convert: % -> InputForm if S has ConvertibleTo InputForm
- from ConvertibleTo InputForm
- copy: % -> %
- from Aggregate
- dictionary: () -> %
- from DictionaryOperations S
- dictionary: List S -> %
- from DictionaryOperations S
- difference: (%, %) -> %
- from SetAggregate S
- difference: (%, S) -> %
- from SetAggregate S
- duplicates: % -> List Record(entry: S, count: NonNegativeInteger)
- from MultiDictionary S
- empty: () -> %
- from Aggregate
- empty?: % -> Boolean
- from Aggregate
- eq?: (%, %) -> Boolean
- from Aggregate
- 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)
- extract!: % -> S
- from BagAggregate S
- find: (S -> Boolean, %) -> Union(S, failed)
- from Collection S
- hash: % -> SingleInteger
- from SetCategory
- hashUpdate!: (HashState, %) -> HashState
- from SetCategory
- insert!: (S, %) -> %
- from BagAggregate S
- insert!: (S, %, NonNegativeInteger) -> %
- from MultiDictionary S
- inspect: % -> S
- from BagAggregate S
- intersect: (%, %) -> %
- from SetAggregate S
- latex: % -> String
- from SetCategory
- less?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- map: (S -> S, %) -> %
- from HomogeneousAggregate S

- members: % -> List S
`members(ms)`

returns a list of the elements of`ms`

*without*their multiplicity. See also parts.- more?: (%, NonNegativeInteger) -> Boolean
- from Aggregate

- multiset: () -> %
`multiset()`

$`D`

creates an empty multiset of domain`D`

.

- multiset: List S -> %
`multiset(ls)`

creates a multiset with elements from`ls`

.

- multiset: S -> %
`multiset(s)`

creates a multiset with singleton`s`

.

- remove!: (S -> Boolean, %, Integer) -> %
`remove!(p, ms, number)`

removes destructively at most`number`

copies of elements`x`

such that`p(x)`

is ``true` if ``number` is positive, all of them if`number`

equals zero, and all but at most`-number`

if`number`

is negative.

- remove!: (S, %, Integer) -> %
`remove!(x, ms, number)`

removes destructively at most`number`

copies of element`x`

if`number`

is positive, all of them if`number`

equals zero, and all but at most`-number`

if`number`

is negative.

- remove: (S -> Boolean, %, Integer) -> %
`remove(p, ms, number)`

removes at most`number`

copies of elements`x`

such that`p(x)`

is ``true` if ``number` is positive, all of them if`number`

equals zero, and all but at most`-number`

if`number`

is negative.

- remove: (S, %, Integer) -> %
`remove(x, ms, number)`

removes at most`number`

copies of element`x`

if`number`

is positive, all of them if`number`

equals zero, and all but at most`-number`

if`number`

is negative.- removeDuplicates!: % -> %
- from MultiDictionary S
- sample: %
- from Aggregate
- set: () -> %
- from SetAggregate S
- set: List S -> %
- from SetAggregate S
- size?: (%, NonNegativeInteger) -> Boolean
- from Aggregate
- subset?: (%, %) -> Boolean
- from SetAggregate S
- symmetricDifference: (%, %) -> %
- from SetAggregate S
- union: (%, %) -> %
- from SetAggregate S
- union: (%, S) -> %
- from SetAggregate S
- union: (S, %) -> %
- from SetAggregate S

ConvertibleTo InputForm if S has ConvertibleTo InputForm

Evalable S if S has Evalable S

InnerEvalable(S, S) if S has Evalable S