Returns the set difference of two objects inheriting from class Set. If y is missing
then the complement of x from its universe is returned.
setcomplement(x, y, simplify = TRUE) # S3 method for Set setcomplement(x, y, simplify = TRUE) # S3 method for Interval setcomplement(x, y, simplify = TRUE) # S3 method for FuzzySet setcomplement(x, y, simplify = TRUE) # S3 method for ConditionalSet setcomplement(x, y, simplify = TRUE) # S3 method for Reals setcomplement(x, y, simplify = TRUE) # S3 method for Rationals setcomplement(x, y, simplify = TRUE) # S3 method for Integers setcomplement(x, y, simplify = TRUE) # S3 method for ComplementSet setcomplement(x, y, simplify = TRUE) # S3 method for Set -(x, y)
| x, y | Set |
|---|---|
| simplify | logical, if |
An object inheriting from Set containing the set difference of elements in x and y.
The difference of two sets, \(X, Y\), is defined as the set of elements that exist in set \(X\) and not \(Y\), $$X-Y = \{z : z \epsilon X \quad and \quad \neg(z \epsilon Y)\}$$
The set difference of two ConditionalSets is defined by combining their defining functions by a negated
'and', !&, operator. See examples.
The complement of fuzzy and crisp sets first coerces fuzzy sets to crisp sets by finding their support.
Other operators:
powerset(),
setintersect(),
setpower(),
setproduct(),
setsymdiff(),
setunion()
# absolute complement setcomplement(Set$new(1, 2, 3, universe = Reals$new())) #> (-∞,1) ∪ (1,2) ∪ (2,3) ∪ (3,+∞) setcomplement(Set$new(1, 2, universe = Set$new(1, 2, 3, 4, 5))) #> {3, 4, 5} # complement of two sets Set$new(-2:4) - Set$new(2:5) #> {-1, -2, 0, 1} setcomplement(Set$new(1, 4, "a"), Set$new("a", 6)) #> {1, 4} # complement of two intervals Interval$new(1, 10) - Interval$new(5, 15) #> [1,5) Interval$new(1, 10) - Interval$new(-15, 15) #> ∅ Interval$new(1, 10) - Interval$new(-1, 2) #> (2,10] # complement of mixed set types Set$new(1:10) - Interval$new(5, 15) #> Called from: FUN(X[[i]], ...) #> debug: if (!testSet(y)) { #> return(FALSE) #> } #> debug: if (testFuzzy(y)) { #> if (!all(y$membership() == 1)) { #> return(FALSE) #> } #> } #> debug: if (testConditionalSet(y)) { #> return(FALSE) #> } else if (testInterval(y)) { #> if (testCountablyFinite(y)) { #> return(all(suppressWarnings(y$elements %in% self$elements & #> self$elements %in% y$elements))) #> } #> else { #> return(FALSE) #> } #> } else if (sum(testEmpty(self), testEmpty(y)) == 1) { #> return(FALSE) #> } else { #> comp <- suppressWarnings(y$.__enclos_env__$private$.str_elements %in% #> private$.str_elements & private$.str_elements %in% y$.__enclos_env__$private$.str_elements) #> return(all(comp)) #> } #> debug: if (testInterval(y)) { #> if (testCountablyFinite(y)) { #> return(all(suppressWarnings(y$elements %in% self$elements & #> self$elements %in% y$elements))) #> } #> else { #> return(FALSE) #> } #> } else if (sum(testEmpty(self), testEmpty(y)) == 1) { #> return(FALSE) #> } else { #> comp <- suppressWarnings(y$.__enclos_env__$private$.str_elements %in% #> private$.str_elements & private$.str_elements %in% y$.__enclos_env__$private$.str_elements) #> return(all(comp)) #> } #> debug: if (testCountablyFinite(y)) { #> return(all(suppressWarnings(y$elements %in% self$elements & #> self$elements %in% y$elements))) #> } else { #> return(FALSE) #> } #> debug: return(FALSE) #> {1, 2, 3, 4} Set$new(5, 7) - Tuple$new(6, 8, 7) #> {5} # FuzzySet-Set returns a FuzzySet FuzzySet$new(1, 0.1, 2, 0.5) - Set$new(2:5) #> {1(0.1)} # Set-FuzzySet returns a Set Set$new(2:5) - FuzzySet$new(1, 0.1, 2, 0.5) #> {3, 4, 5} # complement of conditional sets ConditionalSet$new(function(x, y, simplify = TRUE) x >= y) - ConditionalSet$new(function(x, y, simplify = TRUE) x == y) #> {x ∈ 𝕍, y ∈ 𝕍, simplify ∈ 𝕍 : x >= y & !(x == y)} # complement of special sets Reals$new() - NegReals$new() #> ℝ+ Rationals$new() - PosRationals$new() #> ℚ- Integers$new() - PosIntegers$new() #> ℤ-