Set SΒΆ
sets.spad line 1 [edit on github]
S: SetCategory
A set over a domain S models the usual mathematical notion of a finite set of elements from S. Sets are unordered collections of distinct elements (that is, order and duplication does not matter). The notation set [a, b, c] can be used to create a set and the usual operations such as union and intersection are available to form new sets. If S has OrderdSet, Language{} maintains the entries in sorted order. Specifically, the parts function returns the entries as a list in ascending order and the extract! operation returns the maximum entry. Given two sets s and t where \#s = m and \#t = n, the complexity of s = t is O(min(n, m)) s < t is O(max(n, m)) union(s, t), intersect(s, t), minus(s, t), symmetricDifference(s, t) is O(max(n, m)) member?(x, t) is O(n log n) insert!(x, t) and remove!(x, t) is O(n)
- #: % -> NonNegativeInteger
from Aggregate
- <=: (%, %) -> Boolean
from PartialOrder
- <: (%, %) -> Boolean
from PartialOrder
- >=: (%, %) -> Boolean
from PartialOrder
- >: (%, %) -> Boolean
from PartialOrder
- any?: (S -> Boolean, %) -> Boolean
from HomogeneousAggregate S
- cardinality: % -> NonNegativeInteger
from FiniteSetAggregate S
- coerce: % -> OutputForm
from CoercibleTo OutputForm
- complement: % -> % if S has Finite
from FiniteSetAggregate S
- 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
from FiniteSetAggregate S
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