From 4be194212a7a3d02bacf04b1a892f15c1b3f6291 Mon Sep 17 00:00:00 2001
From: schillic <git@christianschilling.net>
Date: Fri, 13 Dec 2024 19:15:48 +0100
Subject: [PATCH] EmptySet: redefine norm/radius/diameter

---
 src/Sets/EmptySet/diameter.jl | 5 +++--
 src/Sets/EmptySet/norm.jl     | 5 +++--
 src/Sets/EmptySet/radius.jl   | 5 +++--
 test/Sets/EmptySet.jl         | 6 +++---
 4 files changed, 12 insertions(+), 9 deletions(-)

diff --git a/src/Sets/EmptySet/diameter.jl b/src/Sets/EmptySet/diameter.jl
index 1e57ef52bd..ba191aac11 100644
--- a/src/Sets/EmptySet/diameter.jl
+++ b/src/Sets/EmptySet/diameter.jl
@@ -1,3 +1,4 @@
-function diameter(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the diameter of an empty set is undefined"))
+function diameter(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end
diff --git a/src/Sets/EmptySet/norm.jl b/src/Sets/EmptySet/norm.jl
index 53765124de..a1d2d9df1b 100644
--- a/src/Sets/EmptySet/norm.jl
+++ b/src/Sets/EmptySet/norm.jl
@@ -1,3 +1,4 @@
-function norm(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the norm of an empty set is undefined"))
+function norm(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end
diff --git a/src/Sets/EmptySet/radius.jl b/src/Sets/EmptySet/radius.jl
index 6727e5e370..f72e23c1a0 100644
--- a/src/Sets/EmptySet/radius.jl
+++ b/src/Sets/EmptySet/radius.jl
@@ -1,3 +1,4 @@
-function radius(::EmptySet, ::Real=Inf)
-    throw(ArgumentError("the radius of an empty set is undefined"))
+function radius(∅::EmptySet, ::Real=Inf)
+    N = eltype(∅)
+    return zero(N)
 end
diff --git a/test/Sets/EmptySet.jl b/test/Sets/EmptySet.jl
index 0892a36a25..ce68c1e0b3 100644
--- a/test/Sets/EmptySet.jl
+++ b/test/Sets/EmptySet.jl
@@ -37,9 +37,9 @@ for N in [Float64, Rational{Int}, Float32]
 
     # an_element/norm/radius/diameter functions
     @test_throws ArgumentError an_element(E)
-    @test_throws ArgumentError norm(E)
-    @test_throws ArgumentError radius(E)
-    @test_throws ArgumentError diameter(E)
+    @test norm(E) == N(0)
+    @test radius(E) == N(0)
+    @test diameter(E) == N(0)
 
     # vertices / vertices_list
     @test collect(vertices(E)) == vertices_list(E) == Vector{Vector{N}}()