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Raphael Sonabend
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| This package was submitted to CRAN on 2020-07-26. | ||
| Once it is accepted, delete this file and tag the release (commit 5a74439f94). |
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| #' @name Complex | ||
| #' @title Set of Complex Numbers | ||
| #' @description The mathematical set of complex numbers, | ||
| #' defined as the the set of reals with possibly imaginary components. i.e. | ||
| #' \deqn{\\{a + bi \\ : \\ a,b \in R\\}}{{a + bi : a,b \epsilon R}} | ||
| #' where \eqn{R} is the set of reals. | ||
| #' | ||
| #' @details There is no inherent ordering in the set of complex numbers, hence only the `contains` | ||
| #' method is implemented here. | ||
| #' | ||
| #' @family special sets | ||
| #' @export | ||
| Complex <- R6Class("Complex", | ||
| inherit = Set, | ||
| public = list( | ||
| #' @description Create a new `Complex` object. | ||
| #' @return A new `Complex` object. | ||
| initialize = function() { | ||
| private$.properties <- Properties$new(closure = "open", cardinality = Inf) | ||
| invisible(self) | ||
| }, | ||
|
|
||
| #' @description Tests to see if \code{x} is contained in the Set. | ||
| #' | ||
| #' @param x any. Object or vector of objects to test. | ||
| #' @param all logical. If `FALSE` tests each `x` separately. Otherwise returns `TRUE` only if all `x` pass test. | ||
| #' @param bound logical. | ||
| #' | ||
| #' @details \code{x} can be of any type, including a Set itself. \code{x} should be a tuple if | ||
| #' checking to see if it lies within a set of dimension greater than one. To test for multiple \code{x} | ||
| #' at the same time, then provide these as a list. | ||
| #' | ||
| #' If `all = TRUE` then returns `TRUE` if all `x` are contained in the `Set`, otherwise | ||
| #' returns a vector of logicals. For [Interval]s, `bound` is used to specify if elements lying on the | ||
| #' (possibly open) boundary of the interval are considered contained (`bound = TRUE`) or not (`bound = FALSE`). | ||
| #' | ||
| #' @return If \code{all} is `TRUE` then returns `TRUE` if all elements of \code{x} are contained in the `Set`, otherwise | ||
| #' `FALSE.` If \code{all} is `FALSE` then returns a vector of logicals corresponding to each individual | ||
| #' element of \code{x}. | ||
| #' | ||
| #' The infix operator `%inset%` is available to test if `x` is an element in the `Set`, | ||
| #' see examples. | ||
| contains = function(x, all = FALSE, bound = NULL) { | ||
| returner( | ||
| x = sapply(x, is.complex), | ||
| all = all | ||
| ) | ||
| }, | ||
|
|
||
| #' @description Tests if two sets are equal. | ||
| #' @param x [Set] or vector of [Set]s. | ||
| #' @param all logical. If `FALSE` tests each `x` separately. Otherwise returns `TRUE` only if all `x` pass test. | ||
| #' @return If `all` is `TRUE` then returns `TRUE` if all `x` are equal to the Set, otherwise | ||
| #' `FALSE`. If `all` is `FALSE` then returns a vector of logicals corresponding to each individual | ||
| #' element of `x`. | ||
| #' | ||
| #' Infix operators can be used for: | ||
| #' \tabular{ll}{ | ||
| #' Equal \tab `==` \cr | ||
| #' Not equal \tab `!=` \cr | ||
| #' } | ||
| #' | ||
| #' @examples | ||
| #' # Equals | ||
| #' Set$new(1,2)$equals(Set$new(5,6)) | ||
| #' Set$new(1,2)$equals(Interval$new(1,2)) | ||
| #' Set$new(1,2) == Interval$new(1,2, class = "integer") | ||
| #' | ||
| #' # Not equal | ||
| #' !Set$new(1,2)$equals(Set$new(1,2)) | ||
| #' Set$new(1,2) != Set$new(1,5) | ||
| equals = function(x, all = FALSE) { | ||
| ret <- sapply(listify(x), getR6Class) %in% "Complex" | ||
| returner(ret, all) | ||
| }, | ||
|
|
||
| #' @description Test if one set is a (proper) subset of another | ||
| #' @param x any. Object or vector of objects to test. | ||
| #' @param proper logical. If `TRUE` tests for proper subsets. | ||
| #' @param all logical. If `FALSE` tests each `x` separately. Otherwise returns `TRUE` only if all `x` pass test. | ||
| #' @details If using the method directly, and not via one of the operators then the additional boolean | ||
| #' argument `proper` can be used to specify testing of subsets or proper subsets. A Set is a proper | ||
| #' subset of another if it is fully contained by the other Set (i.e. not equal to) whereas a Set is a | ||
| #' (non-proper) subset if it is fully contained by, or equal to, the other Set. | ||
| #' | ||
| #' When calling `$isSubset` on objects inheriting from [Interval], the method treats the interval as if | ||
| #' it is a [Set], i.e. ordering and class are ignored. Use `$isSubinterval` to test if one interval | ||
| #' is a subinterval of another. | ||
| #' | ||
| #' Infix operators can be used for: | ||
| #' \tabular{ll}{ | ||
| #' Subset \tab `<` \cr | ||
| #' Proper Subset \tab `<=` \cr | ||
| #' Superset \tab `>` \cr | ||
| #' Proper Superset \tab `>=` | ||
| #' } | ||
| #' | ||
| #' Every `Set` is a subset of a `Universal`. No `Set` is a super set of a `Universal`, | ||
| #' and only a `Universal` is not a proper subset of a `Universal`. | ||
| #' | ||
| #' @return If `all` is `TRUE` then returns `TRUE` if all `x` are subsets of the Set, otherwise | ||
| #' `FALSE`. If `all` is `FALSE` then returns a vector of logicals corresponding to each individual | ||
| #' element of `x`. | ||
| #' @examples | ||
| #' Set$new(1,2,3)$isSubset(Set$new(1,2), proper = TRUE) | ||
| #' Set$new(1,2) < Set$new(1,2,3) # proper subset | ||
| #' | ||
| #' c(Set$new(1,2,3), Set$new(1)) < Set$new(1,2,3) # not proper | ||
| #' Set$new(1,2,3) <= Set$new(1,2,3) # proper | ||
| isSubset = function(x, proper = FALSE, all = FALSE) { | ||
| stop("Not implemented for complex sets.") | ||
| }, | ||
|
|
||
| #' @description Creates a printable representation of the object. | ||
| #' @param n numeric. Number of elements to display on either side of ellipsis when printing. | ||
| #' @return A character string representing the object. | ||
| strprint = function(n = 2) { | ||
| setSymbol(getR6Class(self)) | ||
| } | ||
| ) | ||
| ) |
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| Original file line number | Diff line number | Diff line change |
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| @@ -0,0 +1,28 @@ | ||
| #' @name Logicals | ||
| #' @title Set of Logicals | ||
| #' @description The `Logicals` is defined as the [Set] containing the elements `TRUE` and `FALSE`. | ||
| #' @family special sets | ||
| #' | ||
| #' @examples | ||
| #' l <- Logicals$new() | ||
| #' print(l) | ||
| #' l$contains(list(TRUE, 1, FALSE)) | ||
| #' @export | ||
| Logicals <- R6::R6Class("Logicals", | ||
| inherit = Set, | ||
| public = list( | ||
| #' @description Create a new `Logicals` object. | ||
| #' @details The Logical set is the set containing `TRUE` and `FALSE`. | ||
| #' @return A new `Logicals` object. | ||
| initialize = function() { | ||
| private$.elements <- list(TRUE, FALSE) | ||
| private$.str_elements <- c("TRUE", "FALSE") | ||
| private$.class <- "logical" | ||
| private$.properties <- Properties$new(closure = "closed", cardinality = 2) | ||
| private$.lower <- TRUE | ||
| private$.upper <- FALSE | ||
| private$.universe <- self | ||
| invisible(self) | ||
| } | ||
| ) | ||
| ) |
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