diff --git a/docs/src/lib/representations.md b/docs/src/lib/representations.md
index 2fb1848ebc..09b0d4b135 100644
--- a/docs/src/lib/representations.md
+++ b/docs/src/lib/representations.md
@@ -24,6 +24,18 @@ support_function
 support_vector
 ```
 
+## LazySet interfaces
+
+```@docs
+AbstractSingleton
+AbstractHPolygon
+AbstractPolygon
+AbstractHyperrectangle
+AbstractPointSymmetric
+AbstractPolytope
+AbstractPointSymmetricPolytope
+```
+
 ## Balls
 
 ### Euclidean norm ball
@@ -33,6 +45,7 @@ Ball2
 dim(::Ball2)
 σ(::AbstractVector{Float64}, ::Ball2)
 ∈(::AbstractVector{Float64}, ::Ball2{Float64})
+center(::Ball2{Float64})
 ```
 
 ### Infinity norm ball
@@ -40,12 +53,16 @@ dim(::Ball2)
 ```@docs
 BallInf
 dim(::BallInf)
-σ(::AbstractVector{Float64}, ::BallInf)
-vertices_list(::BallInf)
+σ(::AbstractVector{Float64}, ::BallInf{Float64})
+∈(::AbstractVector{Float64}, ::BallInf{Float64})
 norm(::BallInf, ::Real=Inf)
 radius(::BallInf, ::Real=Inf)
 diameter(::BallInf, ::Real=Inf)
-∈(::AbstractVector{Float64}, ::BallInf{Float64})
+vertices_list(::BallInf{Float64})
+singleton_list(::BallInf{Float64})
+center(::BallInf{Float64})
+radius_b(::BallInf{Float64})
+radius_b(::BallInf{Float64}, ::Int)
 ```
 
 ### Manhattan norm ball
@@ -53,8 +70,11 @@ diameter(::BallInf, ::Real=Inf)
 ```@docs
 Ball1
 dim(::Ball1)
-σ(::AbstractVector{Float64}, ::Ball1)
+σ(::AbstractVector{Float64}, ::Ball1{Float64})
 ∈(::AbstractVector{Float64}, ::Ball1{Float64})
+vertices_list(::Ball1{Float64})
+singleton_list(::Ball1{Float64})
+center(::Ball1{Float64})
 ```
 
 ### p-norm ball
@@ -64,6 +84,7 @@ Ballp
 dim(::Ballp)
 σ(::AbstractVector{Float64}, ::Ballp)
 ∈(::AbstractVector{Float64}, ::Ballp{Float64})
+center(::Ballp{Float64})
 ```
 
 ## Polygons
@@ -72,24 +93,28 @@ dim(::Ballp)
 
 ```@docs
 HPolygon
-addconstraint!(::HPolygon{Float64}, ::LinearConstraint{Float64})
 dim(::HPolygon)
-σ(::AbstractVector{Float64}, ::HPolygon)
+σ(::AbstractVector{Float64}, ::HPolygon{Float64})
 ∈(::AbstractVector{Float64}, ::HPolygon{Float64})
-tovrep(::HPolygon)
-vertices_list(::HPolygon)
+vertices_list(::HPolygon{Float64})
+singleton_list(::HPolygon{Float64})
+tohrep(::HPolygon{Float64})
+tovrep(::HPolygon{Float64})
+addconstraint!(::HPolygon{Float64}, ::LinearConstraint{Float64})
 ```
 
 ### Optimized constraint representation
 
 ```@docs
 HPolygonOpt
-addconstraint!(::HPolygonOpt{Float64}, ::LinearConstraint{Float64})
 dim(::HPolygonOpt)
 σ(::AbstractVector{Float64}, ::HPolygonOpt{Float64})
 ∈(::AbstractVector{Float64}, ::HPolygonOpt{Float64})
-tovrep(::HPolygonOpt)
-vertices_list(::HPolygonOpt)
+vertices_list(::HPolygonOpt{Float64})
+singleton_list(::HPolygonOpt{Float64})
+tohrep(::HPolygonOpt{Float64})
+tovrep(::HPolygonOpt{Float64})
+addconstraint!(::HPolygonOpt{Float64}, ::LinearConstraint{Float64})
 ```
 
 ### Vertex representation
@@ -97,10 +122,12 @@ vertices_list(::HPolygonOpt)
 ```@docs
 VPolygon
 dim(::VPolygon)
-σ(::AbstractVector{Float64}, ::VPolygon)
-vertices_list(::VPolygon)
-singleton_list(::VPolygon)
+σ(::AbstractVector{Float64}, ::VPolygon{Float64})
 ∈(::AbstractVector{Float64}, ::VPolygon{Float64})
+vertices_list(::VPolygon{Float64})
+singleton_list(::VPolygon{Float64})
+tohrep(::VPolygon{Float64})
+tovrep(::VPolygon{Float64})
 ```
 
 ## Lines and linear constraints
@@ -117,12 +144,16 @@ intersection(::Line{Float64}, L2::Line{Float64})
 Hyperrectangle
 Hyperrectangle(;kwargs...)
 dim(::Hyperrectangle)
-σ(::AbstractVector{Float64}, ::Hyperrectangle)
-vertices_list(::Hyperrectangle)
+σ(::AbstractVector{Float64}, ::Hyperrectangle{Float64})
+∈(::AbstractVector{Float64}, ::Hyperrectangle{Float64})
 norm(::Hyperrectangle, ::Real=Inf)
 radius(::Hyperrectangle, ::Real=Inf)
 diameter(::Hyperrectangle, ::Real=Inf)
-∈(::AbstractVector{Float64}, ::Hyperrectangle{Float64})
+vertices_list(::Hyperrectangle{Float64})
+singleton_list(::Hyperrectangle{Float64})
+center(::Hyperrectangle{Float64})
+radius_b(::Hyperrectangle{Float64})
+radius_b(::Hyperrectangle{Float64}, ::Int)
 high(::Hyperrectangle)
 low(::Hyperrectangle)
 ```
@@ -136,23 +167,42 @@ dim(::EmptySet)
 ∈(::AbstractVector{Float64}, ::EmptySet)
 ```
 
-## ZeroSet
-
-```@docs
-ZeroSet
-dim(::ZeroSet)
-σ(::AbstractVector{Float64}, ::ZeroSet)
-∈(::AbstractVector{Float64}, ::ZeroSet)
-```
-
 ## Singletons
 
 ```@docs
 Singleton
 dim(::Singleton)
-σ(::AbstractVector{Float64}, ::Singleton)
+σ(::AbstractVector{Float64}, ::Singleton{Float64})
 ∈(::AbstractVector{Float64}, ::Singleton{Float64})
 ⊆(::Singleton, ::LazySet)
+norm(::Singleton, ::Real=Inf)
+diameter(::Singleton, ::Real=Inf)
+vertices_list(::Singleton{Float64})
+singleton_list(::Singleton{Float64})
+center(::Singleton{Float64})
+radius_b(::Singleton{Float64})
+radius_b(::Singleton{Float64}, ::Int)
+element(::Singleton{Float64})
+element(::Singleton{Float64}, ::Int)
+```
+
+### ZeroSet
+
+```@docs
+ZeroSet
+dim(::ZeroSet)
+σ(::AbstractVector{Float64}, ::ZeroSet)
+∈(::AbstractVector{Float64}, ::ZeroSet{Float64})
+⊆(::ZeroSet, ::LazySet)
+norm(::ZeroSet, ::Real=Inf)
+diameter(::ZeroSet, ::Real=Inf)
+vertices_list(::ZeroSet{Float64})
+singleton_list(::ZeroSet{Float64})
+center(::ZeroSet{Float64})
+radius_b(::ZeroSet{Float64})
+radius_b(::ZeroSet{Float64}, ::Int)
+element(::ZeroSet{Float64})
+element(::ZeroSet{Float64}, ::Int)
 ```
 
 ## Zonotopes
@@ -160,8 +210,10 @@ dim(::Singleton)
 ```@docs
 Zonotope
 dim(::Zonotope)
-σ(d::AbstractVector{Float64}, Z::Zonotope)
+σ(::AbstractVector{Float64}, Z::Zonotope)
+∈(::AbstractVector{Float64}, ::Zonotope{Float64})
+center(::Zonotope{Float64})
 vertices_list(::Zonotope{Float64})
+singleton_list(::Zonotope{Float64})
 order(::Zonotope)
-∈(::AbstractVector{Float64}, ::Zonotope{Float64})
 ```