R/operation_setpower.R

In set6: R6 Mathematical Sets Interface

#' @name setpower
#' @rdname setpower
#' @param x Set
#' @param power power to raise set to, if `"n"` then a variable dimension set is created,
#' see examples.`
#' @param simplify logical, if `TRUE` returns the result in its simplest (unwrapped) form, usually
#' a `Set`, otherwise an `ExponentSet`.
#' @param nest logical, if `FALSE` (default) returns the n-ary cartesian product, otherwise returns
#' the cartesian product applied n times.
#' [Set]s. See details and examples.
#' @title Power of a Set
#' @return An R6 object of class `Set` or `ExponentSet` inheriting from `ProductSet`.
#' @description A convenience wrapper for the n-ary cartesian product of a `Set` by itself,
#' possibly multiple times.
#' @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.
#'
#' @family operators
#' @examples
#' # Power of a Set
#' setpower(Set$new(1, 2), 3, simplify = FALSE)
#' setpower(Set$new(1, 2), 3, simplify = TRUE)
#' Set$new(1, 2)^3
#'
#' # Power of an interval
#' Interval$new(2, 5)^5
#' Reals$new()^3
#'
#' # Use tuples for contains
#' (PosNaturals$new()^3)$contains(Tuple$new(1, 2, 3))
#'
#' # Power of ConditionalSet is meaningless
#' ConditionalSet$new(function(x) TRUE)^2
#'
#' # Power of FuzzySet
#' FuzzySet$new(1, 0.1, 2, 0.5)^2
#'
#' # Variable length
#' x <- Interval$new(0, 1)^"n"
#' x$contains(Tuple$new(0))
#' x$contains(Tuple$new(0, 1))
#' x$contains(Tuple$new(0, 1, 0, 0, 1, 1, 0))
#' x$contains(list(Tuple$new(0, 2), Tuple$new(1, 1)))
#'
#' @export
setpower <- function(x, power, simplify = FALSE, nest = FALSE) {
  classx <- getR6Class(x)
  if (classx == "Universal") {
    return(x)
  }

  if (power == 0) {
    return(Set$new())
  } else if (power == 1) {
    return(x)
  } else if (power == "n") {
    return(ExponentSet$new(x, power))
  } else if (classx %in% c("Set", "FuzzySet", "Tuple", "FuzzyTuple", "Multiset", "FuzzyMultiset") & simplify) {
    x <- rep(list(x), power)
    return(do.call(setproduct, c(x, list(nest = nest, simplify = TRUE))))
  } else if (classx == "ExponentSet") {
    if (x$power == "n") {
      return(x)
    } else {
      return(ExponentSet$new(x$wrappedSets[[1]], x$power * power))
    }
  } else {
    return(ExponentSet$new(x, power))
  }
}

#' @rdname setpower
#' @export
`^.Set` <- function(x, power) {
  setpower(x, power)
}