# SetOfMIntegersInOneToN(m, n)¶

SetOfMIntegersInOneToN implements the subsets of M integers in the interval [1..n]

=: (%, %) -> Boolean

from BasicType

~=: (%, %) -> Boolean

from BasicType

coerce: % -> OutputForm
convert: % -> InputForm
delta: (%, PositiveInteger, PositiveInteger) -> NonNegativeInteger

delta(S, k, p) returns the number of elements of S which are strictly between p and the k^{th} element of S.

elements: % -> List PositiveInteger

elements(S) returns the list of the elements of S in increasing order.

enumerate: () -> List %

from Finite

enumerate: () -> Vector %

enumerate() returns a vector of all the sets of M integers in 1..n.

hash: % -> SingleInteger

from SetCategory

hashUpdate!: (HashState, %) -> HashState

from SetCategory

incrementKthElement: (%, PositiveInteger) -> Union(%, failed)

incrementKthElement(S, k) increments the k^{th} element of S, and returns “failed” if the result is not a set of M integers in 1..n any more.

index: PositiveInteger -> %

from Finite

latex: % -> String

from SetCategory

lookup: % -> PositiveInteger

from Finite

member?: (PositiveInteger, %) -> Boolean

member?(p, s) returns true is p is in s, false otherwise.

random: () -> %

from Finite

replaceKthElement: (%, PositiveInteger, PositiveInteger) -> Union(%, failed)

replaceKthElement(S, k, p) replaces the k^{th} element of S by p, and returns “failed” if the result is not a set of M integers in 1..n any more.

setOfMinN: List PositiveInteger -> %

setOfMinN([a_1, ..., a_m]) returns the set {a_1, …, a_m}. Error if {a_1, …, a_m} is not a set of M integers in 1..n.

size: () -> NonNegativeInteger

from Finite

smaller?: (%, %) -> Boolean

from Comparable

BasicType

Comparable

Finite

SetCategory