isempty for EmptySet

docs/src/lib/representations.md

@@ -128,6 +128,7 @@ dim(::EmptySet)
 σ(::AbstractVector{Real}, ::EmptySet{Real})
 ∈(::AbstractVector{Real}, ::EmptySet{Real})
 an_element(::EmptySet)
+isempty(::EmptySet)
 norm(::EmptySet, ::Real)
 radius(::EmptySet, ::Real)
 diameter(::EmptySet, ::Real)

src/EmptySet.jl

@@ -1,4 +1,4 @@
-import Base.∈
+import Base: ∈, isempty
 
 export EmptySet, ∅,
        an_element
@@ -96,6 +96,23 @@ function an_element(∅::EmptySet)
     error("an empty set does not have any element")
 end
 
+"""
+    isempty(∅::EmptySet)
+
+Return if the empty set is empty or not.
+
+### Input
+
+- `∅` -- empty set
+
+### Output
+
+`true`.
+"""
+function isempty(∅::EmptySet)
+    return true
+end
+
 """
     norm(S::EmptySet, [p]::Real=Inf)
 

test/unit_EmptySet.jl

@@ -43,6 +43,9 @@ for N in [Float64, Rational{Int}, Float32]
     @test !∈(N[0], E)
     @test !∈(N[0, 0], E)
 
+    # emptiness check
+    @test isempty(E)
+
     # an_element/norm/radius/diameter functions
     @test_throws ErrorException an_element(E)
     @test_throws ErrorException norm(E)