Use technical term 'centrally symmetric' for 'point symmetric'

docs/src/assets/interfaces.graphml

@@ -18,10 +18,10 @@
       <data key="d4"/>
       <data key="d6">
         <y:UMLClassNode>
-          <y:Geometry height="28.0" width="254.0" x="236.0" y="9.0"/>
+          <y:Geometry height="28.0" width="70.0" x="328.0" y="9.0"/>
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@@ -60,10 +60,10 @@
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       <data key="d6">
         <y:UMLClassNode>
-          <y:Geometry height="28.0" width="196.0" x="414.16741690653123" y="82.0"/>
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+          <y:NodeLabel alignment="center" autoSizePolicy="content" fontFamily="Dialog" fontSize="13" fontStyle="bold" hasBackgroundColor="false" hasLineColor="false" height="19.1328125" horizontalTextPosition="center" iconTextGap="4" modelName="custom" textColor="#000000" verticalTextPosition="bottom" visible="true" width="211.3525390625" x="5.32373046875" y="3.0">AbstractCentrallySymmetric<y:LabelModel>
               <y:SmartNodeLabelModel distance="4.0"/>
             </y:LabelModel>
             <y:ModelParameter>
@@ -81,10 +81,10 @@
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       <data key="d6">
         <y:UMLClassNode>
-          <y:Geometry height="28.0" width="262.0" x="232.0" y="149.0"/>
+          <y:Geometry height="28.0" width="286.0" x="220.0" y="149.0"/>
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           <y:BorderStyle color="#000000" type="line" width="1.0"/>
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             </y:LabelModel>
             <y:ModelParameter>

docs/src/lib/interfaces.md

@@ -58,30 +58,30 @@ diameter(::LazySet, ::Real)
 an_element(::LazySet{Real})
 ```
 
-## Point symmetric set
+## Centrally symmetric set
 
-Point symmetric sets such as balls of different norms are characterized by a
+Centrally symmetric sets such as balls of different norms are characterized by a
 center.
 Note that there is a special interface combination
-[Point symmetric polytope](@ref).
+[Centrally symmetric polytope](@ref).
 
 ```@docs
-AbstractPointSymmetric
+AbstractCentrallySymmetric
 ```
 
 This interface defines the following functions:
 
 ```@docs
-dim(::AbstractPointSymmetric)
-an_element(::AbstractPointSymmetric{N}) where {N<:Real}
+dim(::AbstractCentrallySymmetric)
+an_element(::AbstractCentrallySymmetric{N}) where {N<:Real}
 ```
 
 ## Polytope
 
 A polytope has finitely many vertices (*V-representation*) resp. facets
 (*H-representation*).
 Note that there is a special interface combination
-[Point symmetric polytope](@ref).
+[Centrally symmetric polytope](@ref).
 
 ```@docs
 AbstractPolytope
@@ -128,25 +128,26 @@ addconstraint!(::AbstractHPolygon{Real}, ::LinearConstraint{Real})
 constraints_list(::AbstractHPolygon{Real})
 ```
 
-### Point symmetric polytope
+### Centrally symmetric polytope
 
-A point symmetric polytope is a combination of two other interfaces:
-[Point symmetric set](@ref) and [Polytope](@ref).
+A centrally symmetric polytope is a combination of two other interfaces:
+[Centrally symmetric set](@ref) and [Polytope](@ref).
 
 ```@docs
-AbstractPointSymmetricPolytope
+AbstractCentrallySymmetricPolytope
 ```
 
 This interface defines the following functions:
 
 ```@docs
-dim(::AbstractPointSymmetricPolytope)
-an_element(::AbstractPointSymmetricPolytope{N}) where {N<:Real}
+dim(::AbstractCentrallySymmetricPolytope)
+an_element(::AbstractCentrallySymmetricPolytope{N}) where {N<:Real}
 ```
 
 #### Hyperrectangle
 
-A hyperrectangle is a special point symmetric polytope with axis-aligned facets.
+A hyperrectangle is a special centrally symmetric polytope with axis-aligned
+facets.
 
 ```@docs
 AbstractHyperrectangle

docs/src/lib/operations.md

@@ -234,8 +234,8 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * `an_element`
 
 Inherited from [`AbstractHyperrectangle`](@ref):

docs/src/lib/representations.md

@@ -30,8 +30,8 @@ Inherited from [`LazySet`](@ref):
 * [`radius`](@ref radius(::LazySet, ::Real))
 * [`diameter`](@ref diameter(::LazySet, ::Real))
 
-Inherited from [`AbstractPointSymmetric`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetric))
+Inherited from [`AbstractCentrallySymmetric`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetric))
 * `an_element`
 
 ### Infinity norm ball
@@ -50,8 +50,8 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * `an_element`
 
 Inherited from [`AbstractHyperrectangle`](@ref):
@@ -78,8 +78,8 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * `an_element`
 
 ### p-norm ball
@@ -95,8 +95,8 @@ Inherited from [`LazySet`](@ref):
 * [`radius`](@ref radius(::LazySet, ::Real))
 * [`diameter`](@ref diameter(::LazySet, ::Real))
 
-Inherited from [`AbstractPointSymmetric`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetric))
+Inherited from [`AbstractCentrallySymmetric`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetric))
 * `an_element`
 
 ## Ellipsoid
@@ -112,8 +112,8 @@ Inherited from [`LazySet`](@ref):
 * [`radius`](@ref radius(::LazySet, ::Real))
 * [`diameter`](@ref diameter(::LazySet, ::Real))
 
-Inherited from [`AbstractPointSymmetric`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetric))
+Inherited from [`AbstractCentrallySymmetric`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetric))
 * `an_element`
 
 ## Empty set
@@ -182,8 +182,8 @@ Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 * [`linear_map`](@ref linear_map(::AbstractMatrix, ::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * `an_element`
 
 Inherited from [`AbstractHyperrectangle`](@ref):
@@ -389,8 +389,8 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 
 Inherited from [`AbstractHyperrectangle`](@ref):
 * [`norm`](@ref norm(::AbstractHyperrectangle, ::Real))
@@ -457,6 +457,6 @@ Inherited from [`LazySet`](@ref):
 Inherited from [`AbstractPolytope`](@ref):
 * [`singleton_list`](@ref singleton_list(::AbstractPolytope))
 
-Inherited from [`AbstractPointSymmetricPolytope`](@ref):
-* [`dim`](@ref dim(::AbstractPointSymmetricPolytope))
+Inherited from [`AbstractCentrallySymmetricPolytope`](@ref):
+* [`dim`](@ref dim(::AbstractCentrallySymmetricPolytope))
 * `an_element`

docs/src/man/set_operations.md

@@ -67,8 +67,8 @@ The table entries have the following meaning.
 | `LazySet`                    |        |          |      |            |   |
 | `AHPolygon`                  |        |          |      |     x      | x |
 | `AHyperrectangle`            |   x    |    x     |  x   |    (x)     | x |
-| `APointSymmetric`            |        |          |      |     x      |   |
-| `APointSymmetricPolytope`    |        |          |      |     x      |   |
+| `ACentrallySymmetric`        |        |          |      |     x      |   |
+| `ACentrallySymmetricPolytope`|        |          |      |     x      |   |
 | `APolygon`                   |        |          |      |            |   |
 | `APolytope`                  |        |          |      |            |   |
 | `ASingleton`                 |  (x)   |   (x)    | (x)  |     x      | x |
@@ -198,8 +198,8 @@ The table entries consist of subsets of the following list of operations.
 | `LazySet`                    |     |     |  ⊆  |     |      |     |     |(⊆),∩=∅|     |     | (⊆) |     |     |     |     |     | (⊆)  | (⊆)   |     | (⊆)   |     |     |     |     |     |     |     |     |     |     |     |     |     | (⊆) |
 | `AHPolygon`                  | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  | (⊆) | (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  |(⊆,∩=∅)| (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
 | `AHyperrectangle`            | (⊆) | (⊆) |{⊆},∩=∅|(⊆)| (⊆)  | (⊆) | (⊆) |[⊆,∩=∅]| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |(⊆,∩=∅)|(⊆,∩=∅)|(⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
-| `APointSymmetric`            |     |     | (⊆) |     |      |     |     |(⊆,∩=∅)|     |     |     |     |     |     |     |     |      |(⊆,∩=∅)|     |(⊆,∩=∅)|     |     |     |     |     |     |     |     |     |     |     |     |     |     |
-| `APointSymmetricPolytope`    | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  | (⊆) | (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  |(⊆,∩=∅)| (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
+| `ACentrallySymmetric`        |     |     | (⊆) |     |      |     |     |(⊆,∩=∅)|     |     |     |     |     |     |     |     |      |(⊆,∩=∅)|     |(⊆,∩=∅)|     |     |     |     |     |     |     |     |     |     |     |     |     |     |
+| `ACentrallySymmetricPolytope`| (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  | (⊆) | (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  |(⊆,∩=∅)| (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
 | `APolygon`                   | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  | (⊆) | (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  |(⊆,∩=∅)| (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
 | `APolytope`                  |  ⊆  | (⊆) | [⊆] | (⊆) | (⊆)  | (⊆) | (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆)  |(⊆,∩=∅)| (⊆) |(⊆,∩=∅)| (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) | (⊆) |
 | `ASingleton`                 |{⊆},∩=∅|(⊆,∩=∅)|[⊆,∩=∅]|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|[⊆,∩=∅]|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|((⊆,∩=∅))|(⊆,∩=∅)|((⊆,∩=∅))|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|(⊆,∩=∅)|

src/AbstractCentrallySymmetric.jl

@@ -0,0 +1,60 @@
+export AbstractCentrallySymmetric,
+       center,
+       an_element
+
+"""
+    AbstractCentrallySymmetric{N<:Real} <: LazySet{N}
+
+Abstract type for centrally symmetric sets.
+
+### Notes
+
+Every concrete `AbstractCentrallySymmetric` must define the following functions:
+
+- `center(::AbstractCentrallySymmetric{N})::Vector{N}` -- return the center
+    point
+
+```jldoctest
+julia> subtypes(AbstractCentrallySymmetric)
+3-element Array{Any,1}:
+ Ball2
+ Ballp
+ Ellipsoid
+```
+"""
+abstract type AbstractCentrallySymmetric{N<:Real} <: LazySet{N} end
+
+
+"""
+    dim(S::AbstractCentrallySymmetric)::Int
+
+Return the ambient dimension of a centrally symmetric set.
+
+### Input
+
+- `S` -- set
+
+### Output
+
+The ambient dimension of the set.
+"""
+@inline function dim(S::AbstractCentrallySymmetric)::Int
+    return length(center(S))
+end
+
+"""
+    an_element(S::AbstractCentrallySymmetric{N})::Vector{N} where {N<:Real}
+
+Return some element of a centrally symmetric set.
+
+### Input
+
+- `S` -- centrally symmetric set
+
+### Output
+
+The center of the centrally symmetric set.
+"""
+function an_element(S::AbstractCentrallySymmetric{N})::Vector{N} where {N<:Real}
+    return center(S)
+end

src/AbstractCentrallySymmetricPolytope.jl

@@ -0,0 +1,78 @@
+export AbstractCentrallySymmetricPolytope,
+       center,
+       an_element,
+       vertices_list,
+       singleton_list
+
+"""
+    AbstractCentrallySymmetricPolytope{N<:Real} <: AbstractPolytope{N}
+
+Abstract type for centrally symmetric, polytopic sets.
+It combines the `AbstractCentrallySymmetric` and `AbstractPolytope` interfaces.
+Such a type combination is necessary as long as Julia does not support
+[multiple inheritance](https://github.com/JuliaLang/julia/issues/5).
+
+### Notes
+
+Every concrete `AbstractCentrallySymmetricPolytope` must define the following
+functions:
+- from `AbstractCentrallySymmetric`:
+  - `center(::AbstractCentrallySymmetricPolytope{N})::Vector{N}` -- return the
+     center point
+- from `AbstractPolytope`:
+  - `vertices_list(::AbstractCentrallySymmetricPolytope{N})::Vector{Vector{N}}`
+     -- return a list of all vertices
+
+```jldoctest
+julia> subtypes(AbstractCentrallySymmetricPolytope)
+5-element Array{Any,1}:
+ AbstractHyperrectangle
+ Ball1
+ Interval
+ LineSegment
+ Zonotope
+```
+"""
+abstract type AbstractCentrallySymmetricPolytope{N<:Real} <: AbstractPolytope{N}
+end
+
+
+# --- common AbstractCentrallySymmetric functions (copy-pasted) ---
+
+
+"""
+    dim(P::AbstractCentrallySymmetricPolytope)::Int
+
+Return the ambient dimension of a centrally symmetric set.
+
+### Input
+
+- `P` -- set
+
+### Output
+
+The ambient dimension of the set.
+"""
+@inline function dim(P::AbstractCentrallySymmetricPolytope)::Int
+    return length(center(P))
+end
+
+
+"""
+    an_element(P::AbstractCentrallySymmetricPolytope{N})::Vector{N}
+        where {N<:Real}
+
+Return some element of a centrally symmetric polytope.
+
+### Input
+
+- `P` -- centrally symmetric polytope
+
+### Output
+
+The center of the centrally symmetric polytope.
+"""
+function an_element(P::AbstractCentrallySymmetricPolytope{N}
+                   )::Vector{N} where {N<:Real}
+    return center(P)
+end

src/AbstractHyperrectangle.jl

@@ -4,7 +4,7 @@ export AbstractHyperrectangle,
        radius_hyperrectangle
 
 """
-    AbstractHyperrectangle{N<:Real} <: AbstractPointSymmetricPolytope{N}
+    AbstractHyperrectangle{N<:Real} <: AbstractCentrallySymmetricPolytope{N}
 
 Abstract type for hyperrectangular sets.
 
@@ -25,7 +25,7 @@ julia> subtypes(AbstractHyperrectangle)
  SymmetricIntervalHull
 ```
 """
-abstract type AbstractHyperrectangle{N<:Real} <: AbstractPointSymmetricPolytope{N}
+abstract type AbstractHyperrectangle{N<:Real} <: AbstractCentrallySymmetricPolytope{N}
 end