#974 - tohrep and tovrep do not preserve numeric type

src/HPolyhedron.jl

@@ -601,7 +601,11 @@ function tovrep(P::HPoly{N};
     @assert isdefined(@__MODULE__, :Polyhedra) "the function `tovrep` needs " *
                                         "the package 'Polyhedra' to be loaded"
     P = polyhedron(P; backend=backend)
-    return VPolytope(P)
+    Q = VPolytope(P)
+    if Q isa VPolytope{N}
+        return Q
+    end
+    return VPolytope{N}(vertices_list(Q))
 end
 
 """

src/HalfSpace.jl

@@ -1,6 +1,7 @@
 import Base: rand,
              ∈,
-             isempty
+             isempty,
+             convert
 
 export HalfSpace, LinearConstraint,
        an_element,
@@ -31,6 +32,10 @@ struct HalfSpace{N<:Real} <: LazySet{N}
     b::N
 end
 
+function convert(::Type{HalfSpace{N}}, hs::HalfSpace) where {N<:Real}
+    return HalfSpace{N}(hs.a, hs.b)
+end
+
 """
     LinearConstraint
 

src/VPolytope.jl

@@ -273,7 +273,11 @@ function tohrep(P::VPolytope{N};
                 backend=default_polyhedra_backend(P, N)) where {N<:Real}
     @assert isdefined(@__MODULE__, :Polyhedra) "the function `tohrep` needs the " *
                                                "package 'Polyhedra' to be loaded"
-    return HPolytope(polyhedron(P; backend=backend))
+    Q = HPolytope(polyhedron(P; backend=backend))
+    if Q isa HPolytope{N}
+        return Q
+    end
+    return HPolytope{N}(constraints_list(Q))
 end
 
 """

test/unit_HalfSpace.jl

@@ -6,6 +6,11 @@ for N in [Float64, Rational{Int}, Float32]
     normal = ones(N, 3)
     hs = HalfSpace(normal, N(5))
 
+    # numeric-type conversion preserves vector base type
+    hs1 = HalfSpace(spzeros(4), 1.)
+    hs2 = convert(HalfSpace{N}, hs1)
+    @test hs2.a isa SparseVector{N}
+
     # dimension
     @test dim(hs) == 3
 

test/unit_Polytope.jl

@@ -190,8 +190,8 @@ if test_suite_polyhedra
         A = [N(0) N(-1); N(-1) N(0); N(1) N(1)]
         b = N[-0.25, -0.25, -0]
         P = HPolytope(A, b)
-        @test tovrep(P) isa VPolytope
-        @test tohrep(P) isa HPolytope # test no-op
+        @test tovrep(P) isa VPolytope{N}
+        @test tohrep(P) isa HPolytope{N}  # no-op
 
         # checking for emptiness
         P = HPolytope([LinearConstraint(N[1, 0], N(0))])    # x <= 0
@@ -246,7 +246,7 @@ if test_suite_polyhedra
 
         # tohrep from VPolytope
         P = VPolytope([v1, v2, v3, v4, v5])
-        @test tohrep(P) isa HPolytope
-        @test tovrep(P) isa VPolytope # no-op
+        @test tohrep(P) isa HPolytope{N}
+        @test tovrep(P) isa VPolytope{N}  # no-op
     end
 end