Finite

catdef.spad line 610 [edit on github]

The category of domains composed of a finite set of elements. We include the functions lookup and index to give a bijection between the finite set and an initial segment of positive integers.

= : (%, %) -> Boolean

from BasicType

coerce : % -> OutputForm

from CoercibleTo(OutputForm)

convert : % -> InputForm

from ConvertibleTo(InputForm)

enumerate : () -> List(%)

enumerate() returns list of elements of the set.

hash : % -> SingleInteger

from Hashable

hashUpdate! : (HashState, %) -> HashState

from Hashable

index : PositiveInteger -> %

index(i) takes a positive integer i less than or equal to size() and returns the i-th element of the set. This operation establishes a bijection between the elements of the finite set and 1..size().

latex : % -> String

from SetCategory

lookup : % -> PositiveInteger

lookup(x) returns a positive integer such that x = index lookup x.

random : () -> %

random() returns a random element from the set.

size : () -> NonNegativeInteger

size() returns the number of elements in the set.

smaller? : (%, %) -> Boolean

from Comparable

~= : (%, %) -> Boolean

from BasicType

Comparable

CoercibleTo(OutputForm)

SetCategory

Hashable

BasicType

ConvertibleTo(InputForm)