AbstractAffineMap: add isuniversal method

docs/src/lib/interfaces/AbstractAffineMap.md

@@ -89,6 +89,18 @@ isempty(::AbstractAffineMap)
 CurrentModule = LazySets.API
 ```
 ```@docs; canonical=false
+isuniversal(::LazySet)
+```
+```@meta
+CurrentModule = LazySets
+```
+```@docs
+isuniversal(::AbstractAffineMap)
+```
+```@meta
+CurrentModule = LazySets.API
+```
+```@docs; canonical=false
 ∈(::AbstractVector, ::LazySet)
 ```
 ```@meta

src/Interfaces/AbstractAffineMap.jl

@@ -267,6 +267,28 @@ function constraints_list(am::AbstractAffineMap)
                                          vector(am))
 end
 
+"""
+# Extended help
+
+    isuniversal(am::AbstractAffineMap)
+
+### Algorithm
+
+An affine map is universal iff the wrapped set is universal and the matrix does
+not map any dimension to zero.
+"""
+function isuniversal(am::AbstractAffineMap)
+    if isuniversal(set(am))
+        for row in eachrow(matrix(am))
+            if all(isapproxzero, row)
+                return false
+            end
+        end
+        return true
+    end
+    return false
+end
+
 function linear_map(M::AbstractMatrix, am::AbstractAffineMap)
     return affine_map(M * matrix(am), set(am), M * vector(am))
 end

test/LazyOperations/AffineMap.jl

@@ -53,6 +53,14 @@ for N in [Float64, Rational{Int}, Float32]
     @test !isempty(am)
     @test isempty(AffineMap(M, EmptySet{N}(2), v))
 
+    # isuniversal
+    @test !isuniversal(am)
+    U = Universe{N}(3)
+    M = N[1 0 0; 0 0 0; 0 0 1]
+    @test !isuniversal(M * U + v)
+    M = N[1 2 3; -1 -2 -3; 0 0 1]
+    @test isuniversal(M * U + v)
+
     # containment
     L = LineSegment(N[1, 0], N[2, 0])
     b2 = N[1, 0]