Power of a Set

A convenience wrapper for the n-ary cartesian product of a Set by itself, possibly multiple times.

setpower(x, power, simplify = FALSE, nest = FALSE)

# S3 method for Set
^(x, power)

Arguments

x	Set
power	power to raise set to, if "n" then a variable dimension set is created, see examples.`
simplify	logical, if TRUE returns the result in its simplest (unwrapped) form, usually a Set, otherwise an ExponentSet.
nest	logical, if FALSE (default) returns the n-ary cartesian product, otherwise returns the cartesian product applied n times. Sets. See details and examples.

Value

An R6 object of class Set or ExponentSet inheriting from ProductSet.

Details

See the details of setproduct for a longer discussion on the use of the nest argument, in particular with regards to n-ary cartesian products vs. 'standard' cartesian products.

See also

Other operators: powerset(), setcomplement(), setintersect(), setproduct(), setsymdiff(), setunion()

Examples

# Power of a Set
setpower(Set$new(1, 2), 3, simplify = FALSE)
#> {1, 2}^3 
setpower(Set$new(1, 2), 3, simplify = TRUE)
#> {(1, 1, 1), (1, 1, 2),...,(2, 2, 1), (2, 2, 2)} 
Set$new(1, 2)^3
#> {1, 2}^3 

# Power of an interval
Interval$new(2, 5)^5
#> [2,5]^5 
Reals$new()^3
#> ℝ^3 

# Use tuples for contains
(PosNaturals$new()^3)$contains(Tuple$new(1, 2, 3))
#> [1] TRUE

# Power of ConditionalSet is meaningless
ConditionalSet$new(function(x) TRUE)^2
#> {x ∈ 𝕍}^2 

# Power of FuzzySet
FuzzySet$new(1, 0.1, 2, 0.5)^2
#> {1(0.1), 2(0.5)}^2 

# Variable length
x <- Interval$new(0, 1)^"n"
x$contains(Tuple$new(0))
#> [1] TRUE
x$contains(Tuple$new(0, 1))
#> [1] TRUE
x$contains(Tuple$new(0, 1, 0, 0, 1, 1, 0))
#> [1] TRUE
x$contains(list(Tuple$new(0, 2), Tuple$new(1, 1)))
#> [1] FALSE  TRUE