Improve stability of tests in PolyhedralGeometry (#4197)

* introduced helper functions for stable tests in polyhedral geometry, applied to test/polyhedron.jl

* increased stability for cone tests

* increased stability for extended tests

* increased stability for polyhedral_fan tests

* increased stability for scalar_types tests

* increased stability for polyhedral_complex tests

* increased stability for subdivision_of_points tests

* improved == for RayVector; forced RayVector != PointVector

* fixed comparison between RayVectors; comparison between PointVector and RayVector now throws an error

* fixed formatting for iterators.jl

* added and adjusted commented test in cone.jl

* increased code coverage for changes in iterators.jl

* improved comparison between RayVectors

* re-added test for matrix(ZZ, rays(Cone6))

* adjusted test for weights in subdivision_of_points.jl

* improved comparison between RayVectors and added additional tests

src/PolyhedralGeometry/iterators.jl

@@ -85,6 +85,27 @@ Return a `RayVector` resembling a ray from the origin through the point whose co
 """
 ray_vector
 
+function Base.:(==)(x::RayVector, y::RayVector)
+  ix = findfirst(!is_zero, x)
+  iy = findfirst(!is_zero, y)
+  ix == iy || return false
+  isnothing(ix) && return true
+  sign(x[ix]) == sign(y[iy]) || return false
+  return y[iy] * x.p == x[ix] * y.p
+end
+
+function Base.:(==)(x::RayVector, y::AbstractVector)
+  ry = ray_vector(coefficient_field(x), y)
+  return x == ry
+end
+
+Base.:(==)(x::AbstractVector, y::RayVector) = y == x
+
+Base.:(==)(::PointVector, ::RayVector) =
+  throw(ArgumentError("Cannot compare PointVector to RayVector"))
+Base.:(==)(::RayVector, ::PointVector) =
+  throw(ArgumentError("Cannot compare PointVector to RayVector"))
+
 ################################################################################
 ######## Halfspaces and Hyperplanes
 ################################################################################

test/PolyhedralGeometry/cone.jl

@@ -28,43 +28,38 @@
     if T == QQFieldElem
       @test hilbert_basis(Cone1) isa SubObjectIterator{PointVector{ZZRingElem}}
       @test length(hilbert_basis(Cone1)) == 2
-      @test hilbert_basis(Cone1) == [[1, 0], [0, 1]]
-      @test generator_matrix(hilbert_basis(Cone1)) == matrix(QQ, [1 0; 0 1])
+      @test issetequal(hilbert_basis(Cone1), ray_vector.(Ref(ZZ), [[1, 0], [0, 1]]))
+      @test generator_matrix(hilbert_basis(Cone1)) == _oscar_matrix_from_property(ZZ, hilbert_basis(Cone1))
     end
     @test n_rays(Cone1) == 2
     @test rays(RayVector{T}, Cone1) isa SubObjectIterator{RayVector{T}}
     @test rays(Cone1) isa SubObjectIterator{RayVector{T}}
     @test rays(RayVector, Cone1) isa SubObjectIterator{RayVector{T}}
-    @test vector_matrix(rays(Cone1)) == matrix(f, [1 0; 0 1])
+    @test issetequal(rays(Cone1), ray_vector.(Ref(f), [[1, 0], [0, 1]]))
+    @test vector_matrix(rays(Cone1)) == _oscar_matrix_from_property(f, rays(Cone1))
     if T == QQFieldElem
-      @test matrix(QQ, rays(Cone1)) == matrix(QQ, [1 0; 0 1])
-      @test matrix(ZZ, rays(Cone6)) == matrix(ZZ, [2 3; 2 5])
+      @test matrix(QQ, rays(Cone1)) == _oscar_matrix_from_property(f, rays(Cone1))
+      let r = rays(Cone6)
+        m = matrix(ZZ, r[1] == [1//3, 1//2] ? [2 3; 2 5] : [2 5; 2 3])
+        @test matrix(ZZ, rays(Cone6)) == m
+      end
     end
     @test length(rays(Cone1)) == 2
-    @test rays(Cone1) == [[1, 0], [0, 1]]
-    for S in [LinearHalfspace{T}, Cone{T}]
+    for S in [LinearHalfspace{T},
+                     Cone{T}]
       @test facets(S, Cone1) isa SubObjectIterator{S}
       @test length(facets(S, Cone1)) == 2
-      if T == QQFieldElem
-        @test linear_inequality_matrix(facets(S, Cone1)) == matrix(QQ, [-1 0; 0 -1])
-        @test Oscar.linear_matrix_for_polymake(facets(S, Cone1)) == [-1 0; 0 -1]
-        @test ray_indices(facets(S, Cone1)) == IncidenceMatrix([[2], [1]])
-        @test IncidenceMatrix(facets(S, Cone1)) == IncidenceMatrix([[2], [1]])
-        if S == LinearHalfspace{T}
-          @test facets(S, Cone1) == linear_halfspace.([f], [[-1, 0], [0, -1]])
-        end
+      if S == LinearHalfspace{T}
+        @test issetequal(facets(S, Cone1), linear_halfspace.(Ref(f), [[-1, 0], [0, -1]]))
       else
-        @test linear_inequality_matrix(facets(S, Cone1)) == matrix(f, [0 -1; -1 0])
-        @test Oscar.linear_matrix_for_polymake(facets(S, Cone1)) == [0 -1; -1 0]
-        @test ray_indices(facets(S, Cone1)) == IncidenceMatrix([[1], [2]])
-        @test IncidenceMatrix(facets(S, Cone1)) == IncidenceMatrix([[1], [2]])
-        if S == LinearHalfspace{T}
-          @test facets(S, Cone1) == linear_halfspace.([f], [[0, -1], [-1, 0]])
-        end
+        @test issetequal(facets(S, Cone1), positive_hull.(Ref(f), [[1 0], [0 1]]))
       end
+      @test linear_inequality_matrix(facets(S, Cone1)) == _oscar_matrix_from_property(f, facets(S, Cone1))
+      @test Oscar.linear_matrix_for_polymake(facets(S, Cone1)) == _polymake_matrix_from_property(facets(S, Cone1))
+      @test _check_im_perm_rows(ray_indices(facets(S, Cone1)), [[1], [2]])
+      @test _check_im_perm_rows(IncidenceMatrix(facets(S, Cone1)), [[1], [2]])
     end
-    @test facets(IncidenceMatrix, Cone1) ==
-      IncidenceMatrix(T == QQFieldElem ? [[2], [1]] : [[1], [2]])
+    @test _check_im_perm_rows(facets(IncidenceMatrix, Cone1), [[1], [2]])
     @test facets(Halfspace, Cone1) isa SubObjectIterator{LinearHalfspace{T}}
     @test facets(Cone1) isa SubObjectIterator{LinearHalfspace{T}}
     @test linear_span(Cone4) isa SubObjectIterator{LinearHyperplane{T}}
@@ -92,43 +87,32 @@
     end
     @test length(lineality_space(Cone2)) == 1
     @test lineality_space(Cone2) == [L[1, :]]
-    @test vector_matrix(rays(Cone4)) == matrix(f, R)
+    @test vector_matrix(rays(Cone4)) == _oscar_matrix_from_property(f, rays(Cone4))
     @test codim(Cone4) == 1
     @test codim(Cone3) == 0
     @test faces(Cone2, 2) isa SubObjectIterator{Cone{T}}
     @test length(faces(Cone2, 2)) == 2
     @test faces(Cone4, 1) isa SubObjectIterator{Cone{T}}
     @test length(faces(Cone4, 1)) == 2
-    if T == QQFieldElem
-      @test faces(Cone2, 2) == positive_hull.(T, [[0 0 1], [1 0 0]], [[0 1 0]])
-      @test ray_indices(faces(Cone2, 2)) == IncidenceMatrix([[2], [1]])
-      @test IncidenceMatrix(faces(Cone2, 2)) == IncidenceMatrix([[2], [1]])
-      @test faces(IncidenceMatrix, Cone2, 2) == IncidenceMatrix([[2], [1]])
-      @test faces(Cone4, 1) == positive_hull.(T, [[0 0 1], [1 0 0]])
-      @test ray_indices(faces(Cone4, 1)) == IncidenceMatrix([[2], [1]])
-      @test IncidenceMatrix(faces(Cone4, 1)) == IncidenceMatrix([[2], [1]])
-      @test faces(IncidenceMatrix, Cone4, 1) == IncidenceMatrix([[2], [1]])
-    else
-      @test faces(Cone2, 2) == positive_hull.([f], [[1 0 0], [0 0 1]], [[0 1 0]])
-      @test ray_indices(faces(Cone2, 2)) == IncidenceMatrix([[1], [2]])
-      @test IncidenceMatrix(faces(Cone2, 2)) == IncidenceMatrix([[1], [2]])
-      @test faces(IncidenceMatrix, Cone2, 2) == IncidenceMatrix([[1], [2]])
-      @test faces(Cone4, 1) == positive_hull.([f], [[1 0 0], [0 0 1]])
-      @test ray_indices(faces(Cone4, 1)) == IncidenceMatrix([[1], [2]])
-      @test IncidenceMatrix(faces(Cone4, 1)) == IncidenceMatrix([[1], [2]])
-      @test faces(IncidenceMatrix, Cone4, 1) == IncidenceMatrix([[1], [2]])
-    end
-    @test IncidenceMatrix(faces(Cone5, 1)) == IncidenceMatrix([[1], [2], [3], [4]])
+    @test issetequal(faces(Cone2, 2), positive_hull.(Ref(f), [[1 0 0], [0 0 1]], [[0 1 0]]))
+    @test _check_im_perm_rows(ray_indices(faces(Cone2, 2)), [[1], [2]])
+    @test _check_im_perm_rows(IncidenceMatrix(faces(Cone2, 2)), [[1], [2]])
+    @test _check_im_perm_rows(faces(IncidenceMatrix, Cone2, 2), [[1], [2]])
+    @test issetequal(faces(Cone4, 1), positive_hull.(Ref(f), [[0 0 1], [1 0 0]]))
+    @test _check_im_perm_rows(ray_indices(faces(Cone4, 1)), [[1], [2]])
+    @test _check_im_perm_rows(IncidenceMatrix(faces(Cone4, 1)), [[1], [2]])
+    @test _check_im_perm_rows(faces(IncidenceMatrix, Cone4, 1), [[1], [2]])
+    @test _check_im_perm_rows(IncidenceMatrix(faces(Cone5, 1)), [[1], [2], [3], [4]])
     @test isnothing(faces(Cone2, 1))
 
     @test f_vector(Cone5) == [4, 4]
     @test f_vector(Cone2) == [0, 2]
     @test lineality_dim(Cone5) == 0
     @test lineality_dim(Cone2) == 1
-    @test facet_degrees(Cone5)[1] == 2
-    @test facet_degrees(Cone6)[1] == 1
-    @test ray_degrees(Cone5)[1] == 2
-    @test ray_degrees(Cone6)[1] == 1
+    @test facet_degrees(Cone5) == fill(2, 4)
+    @test facet_degrees(Cone6) == fill(1, 2)
+    @test ray_degrees(Cone5) == fill(2, 4)
+    @test ray_degrees(Cone6) == fill(1, 2)
 
     @test n_facets(Cone5) == 4
     @test relative_interior_point(Cone1) == f.([1//2, 1//2])

test/PolyhedralGeometry/extended.jl

@@ -83,29 +83,25 @@
     f = sum([x; 1])^2 + x[1]^4 * x[2] * 3
     newt = newton_polytope(f)
     @test dim(newt) == 2
-    @test point_matrix(vertices(newt)) == matrix(QQ, [4 1; 2 0; 0 2; 0 0])
+    @test issetequal(vertices(newt), point_vector.(Ref(QQ), [[4, 1], [2, 0], [0, 2], [0, 0]]))
   end
 
   @testset "Construct from QQFieldElem" begin
     A = zeros(Oscar.QQ, 3, 2)
     A[1, 1] = 1
     A[3, 2] = 4
-    @test point_matrix(vertices(convex_hull(A))) == matrix(QQ, [1 0; 0 0; 0 4])
+    @test issetequal(vertices(convex_hull(A)), point_vector.(Ref(QQ), [[1, 0], [0, 0], [0, 4]]))
 
-    lhs, rhs = halfspace_matrix_pair(facets(polyhedron(A, [1, 2, -3])))
-    @test lhs == matrix(QQ, [1 0; 0 4])
-    @test rhs == [1, -3]
+    @test issetequal(facets(polyhedron(A, [1, 2, -3])), [affine_halfspace(QQ, [1, 0], 1), affine_halfspace(QQ, [0, 4], -3)])
   end
 
   @testset "Construct from ZZRingElem" begin
     A = zeros(Oscar.ZZ, 3, 2)
     A[1, 1] = 1
     A[3, 2] = 4
-    @test point_matrix(vertices(convex_hull(A))) == matrix(QQ, [1 0; 0 0; 0 4])
+    @test issetequal(vertices(convex_hull(A)), point_vector.(Ref(QQ), [[1, 0], [0, 0], [0, 4]]))
 
-    lhs, rhs = halfspace_matrix_pair(facets(polyhedron(A, [1, 2, -3])))
-    @test lhs == matrix(QQ, [1 0; 0 4])
-    @test rhs == [1, -3]
+    @test issetequal(facets(polyhedron(A, [1, 2, -3])), [affine_halfspace(QQ, [1, 0], 1), affine_halfspace(QQ, [0, 4], -3)])
   end
 
   @testset "SubObjectIterator/Matrix compatibility" begin

test/PolyhedralGeometry/polyhedral_complex.jl

@@ -34,44 +34,36 @@
 
   # test constructor with re-arranged arguments
   let PCF2 = polyhedral_complex(f, -P[1:3, :], I[:, 1:3], -P[4:4, :], I[:, 4:4])
-    @test vertices(PCF) == vertices(PCF2)
-    @test rays(PCF) == rays(PCF2)
-    @test IncidenceMatrix(maximal_polyhedra(PCF)) ==
-      IncidenceMatrix(maximal_polyhedra(PCF2))
+    @test issetequal(vertices(PCF), vertices(PCF2))
+    @test issetequal(rays(PCF), rays(PCF2))
+    @test issetequal(maximal_polyhedra(PCF), maximal_polyhedra(PCF2))
   end
 
   @testset "core functionality" begin
     @test ambient_dim(PC) == 2
     @test vertices(PC) isa SubObjectIterator{PointVector{T}}
     @test length(vertices(PC)) == 4
-    @test point_matrix(vertices(PC)) == matrix(f, P)
-    @test vertices(PC) == [[0, 0], [1, 0], [0, 1], [1, 1]]
+    @test issetequal(vertices(PC), point_vector.(Ref(f), [[0, 0], [1, 0], [0, 1], [1, 1]]))
+    @test point_matrix(vertices(PC)) == _oscar_matrix_from_property(f, vertices(PC))
     @test rays(PCF) isa SubObjectIterator{RayVector{T}}
     @test length(rays(PCF)) == 1
     @test rays(PCF) == [[-1, -1]]
     @test vector_matrix(rays(PCF)) == matrix(f, [-1 -1])
     @test vertices_and_rays(PCFL) isa SubObjectIterator{Union{RayVector{T},PointVector{T}}}
     @test length(vertices_and_rays(PCFL)) == 4
-    @test vertices_and_rays(PCFL) == [[0, 0, 0], [1, 0, 0], [0, 1, 0], [1, 1, 0]]
-    @test typeof.(vertices_and_rays(PCFL)) ==
-      [PointVector{T}, PointVector{T}, PointVector{T}, RayVector{T}]
-    @test vector_matrix(vertices_and_rays(PCFL)) == matrix(f, P2)
+    @test issetequal(vertices_and_rays(PCFL),  [point_vector(f, [0, 0, 0]), point_vector(f, [1, 0, 0]), point_vector(f, [0, 1, 0]), ray_vector(f, [1, 1, 0])])
+    @test vector_matrix(vertices_and_rays(PCFL)) == _oscar_matrix_from_property(f, vertices_and_rays(PCFL))
     @test maximal_polyhedra(PC) isa SubObjectIterator{Polyhedron{T}}
     @test length(maximal_polyhedra(PC)) == 2
-    @test maximal_polyhedra(PC) == convex_hull.([f], [P[1:3, :], P[[2, 4], :]])
+    @test issetequal(maximal_polyhedra(PC), convex_hull.([f], [P[1:3, :], P[[2, 4], :]]))
     @test number_of_maximal_polyhedra(PC) == 2
     @test is_simplicial(PC)
     @test !is_pure(PCL)
     @test dim(PCL) == 3
     @test polyhedra_of_dim(PC, 1) isa SubObjectIterator{Polyhedron{T}}
     @test length(polyhedra_of_dim(PC, 1)) == 4
-    if T == QQFieldElem
-      @test polyhedra_of_dim(PC, 1) ==
-        convex_hull.(T, [P[[2, 4], :], P[[1, 3], :], P[[1, 2], :], P[[2, 3], :]])
-    else
-      @test polyhedra_of_dim(PC, 1) ==
-        convex_hull.([f], [P[[2, 4], :], P[[1, 3], :], P[[2, 3], :], P[[1, 2], :]])
-    end
+    @test issetequal(polyhedra_of_dim(PC, 1),
+                     convex_hull.(Ref(f), [P[[2, 4], :], P[[1, 3], :], P[[2, 3], :], P[[1, 2], :]]))
     @test lineality_space(PCL) isa SubObjectIterator{RayVector{T}}
     @test length(lineality_space(PCL)) == 1
     @test lineality_space(PCL) == [L[:]]
@@ -125,7 +117,7 @@
       @test dim(F) == dim(PC)
       @test ambient_dim(F) == ambient_dim(PC)
       @test lineality_dim(F) == lineality_dim(PC)
-      @test matrix(f, rays(F)) == matrix(f, rays(PC))
+      @test issetequal(rays(F), rays(PC))
       @test n_maximal_cones(F) == n_maximal_polyhedra(PC)
       vrep = PolyhedralComplex{T}(
         Polymake.fan.PolyhedralComplex(;

test/PolyhedralGeometry/polyhedral_fan.jl

@@ -28,10 +28,10 @@
     if T == QQFieldElem
       @test is_smooth(NFsquare)
     end
-    @test vector_matrix(rays(NFsquare)) == matrix(f, [1 0; -1 0; 0 1; 0 -1])
     @test rays(NFsquare) isa SubObjectIterator{RayVector{T}}
     @test length(rays(NFsquare)) == 4
-    @test rays(NFsquare) == [[1, 0], [-1, 0], [0, 1], [0, -1]]
+    @test issetequal(rays(NFsquare), ray_vector.(Ref(f), [[1, 0], [-1, 0], [0, 1], [0, -1]]))
+    @test vector_matrix(rays(NFsquare)) == _oscar_matrix_from_property(f, rays(NFsquare))
     @test is_regular(NFsquare)
     @test is_complete(NFsquare)
     @test !is_complete(F0)
@@ -45,25 +45,23 @@
     @test length(RMLF2[:rays_modulo_lineality]) == 2
     @test maximal_cones(F1) isa SubObjectIterator{Cone{T}}
     @test dim.(maximal_cones(F1)) == [2, 2]
-    @test ray_indices(maximal_cones(F1)) == incidence1
-    @test IncidenceMatrix(maximal_cones(F1)) == incidence1
-    @test maximal_cones(IncidenceMatrix, F1) == incidence1
+    @test _check_im_perm_rows(ray_indices(maximal_cones(F1)), incidence1)
+    @test _check_im_perm_rows(IncidenceMatrix(maximal_cones(F1)), incidence1)
+    @test _check_im_perm_rows(maximal_cones(IncidenceMatrix, F1), incidence1)
     @test number_of_maximal_cones(F1) == 2
     @test lineality_space(F2) isa SubObjectIterator{RayVector{T}}
-    @test generator_matrix(lineality_space(F2)) == matrix(f, L)
-    if T == QQFieldElem
-      @test matrix(QQ, lineality_space(F2)) == matrix(QQ, L)
-    end
     @test length(lineality_space(F2)) == 1
     @test lineality_space(F2) == [L[:]]
+    @test generator_matrix(lineality_space(F2)) == matrix(f, L)
+    @test matrix(f, lineality_space(F2)) == matrix(f, L)
     @test cones(F2, 2) isa SubObjectIterator{Cone{T}}
     @test size(cones(F2, 2)) == (2,)
     @test lineality_space(cones(F2, 2)[1]) == [[0, 1, 0]]
     @test rays.(cones(F2, 2)) == [[], []]
     @test isnothing(cones(F2, 1))
-    @test ray_indices(cones(F1, 2)) == incidence1
-    @test IncidenceMatrix(cones(F1, 2)) == incidence1
-    @test cones(IncidenceMatrix, F1, 2) == incidence1
+    @test _check_im_perm_rows(ray_indices(cones(F1, 2)), incidence1)
+    @test _check_im_perm_rows(IncidenceMatrix(cones(F1, 2)), incidence1)
+    @test _check_im_perm_rows(cones(IncidenceMatrix, F1, 2), incidence1)
 
     II = ray_indices(maximal_cones(NFsquare))
     NF0 = polyhedral_fan(II, rays(NFsquare))
@@ -75,16 +73,16 @@
     end
     @test f_vector(NFsquare) == [4, 4]
     @test rays(F1NR) == collect(eachrow(I3))
-    @test ray_indices(maximal_cones(F1NR)) == incidence1
-    @test IncidenceMatrix(maximal_cones(F1NR)) == incidence1
+    @test _check_im_perm_rows(ray_indices(maximal_cones(F1NR)), incidence1)
+    @test _check_im_perm_rows(IncidenceMatrix(maximal_cones(F1NR)), incidence1)
     @test n_rays(F2NR) == 0
     @test lineality_dim(F2NR) == 1
     RMLF2NR = rays_modulo_lineality(F2NR)
     @test length(RMLF2NR[:rays_modulo_lineality]) == 2
     @test RMLF2NR[:rays_modulo_lineality] == collect(eachrow(R))
     @test lineality_space(F2NR) == collect(eachrow(L))
-    @test ray_indices(maximal_cones(F2NR)) == incidence2
-    @test IncidenceMatrix(maximal_cones(F2NR)) == incidence2
+    @test _check_im_perm_rows(ray_indices(maximal_cones(F2NR)), incidence2)
+    @test _check_im_perm_rows(IncidenceMatrix(maximal_cones(F2NR)), incidence2)
 
     C = positive_hull(f, identity_matrix(ZZ, 0))
     pf = polyhedral_fan(C)

test/PolyhedralGeometry/polyhedron.jl

@@ -37,14 +37,6 @@
   @test nrows(Oscar.pm_object(pf3).INEQUALITIES) == 4
   @test n_vertices(pf3) == 1
 
-  function _check_im_perm_rows(inc::IncidenceMatrix, o)
-    oinc = IncidenceMatrix(o)
-    nr = nrows(inc)
-    nr == nrows(oinc) &&
-      issetequal(Polymake.row.(Ref(inc), 1:nr),
-                 Polymake.row.(Ref(oinc), 1:nr))
-  end
-
   @testset "core functionality" begin
     @test matrix(f, rays(Q1)) * v == T[f(2)]
     @test issetequal(matrix(f, vertices(Q1)) * v, T[f(1), f(0), f(1)])
@@ -55,20 +47,20 @@
     @test n_vertices(Q0) == 3
     @test n_vertices.(faces(Q0, 1)) == [2, 2, 2]
       @test lattice_points(Q0) isa SubObjectIterator{PointVector{ZZRingElem}}
-      @test point_matrix(lattice_points(Q0)) isa MatElem{ZZRingElem}
-      @test matrix(ZZ, lattice_points(Q0)) isa MatElem{ZZRingElem}
       @test length(lattice_points(Q0)) == 3
       @test issetequal(lattice_points(Q0), point_vector.(Ref(ZZ), [[0, 0], [0, 1], [1, 0]]))
+      @test point_matrix(lattice_points(Q0)) == _oscar_matrix_from_property(ZZ, lattice_points(Q0))
+      @test matrix(ZZ, lattice_points(Q0)) == _oscar_matrix_from_property(ZZ, lattice_points(Q0))
       @test interior_lattice_points(square) isa SubObjectIterator{PointVector{ZZRingElem}}
       @test point_matrix(interior_lattice_points(square)) == matrix(ZZ, [0 0])
       @test matrix(ZZ, interior_lattice_points(square)) == matrix(ZZ, [0 0])
       @test length(interior_lattice_points(square)) == 1
       @test interior_lattice_points(square) == [[0, 0]]
       @test boundary_lattice_points(square) isa SubObjectIterator{PointVector{ZZRingElem}}
-      @test point_matrix(boundary_lattice_points(square)) isa MatElem{ZZRingElem}
       @test length(boundary_lattice_points(square)) == 8
       @test issetequal(boundary_lattice_points(square),
                            point_vector.(Ref(ZZ), [[-1, -1], [-1, 0], [-1, 1], [0, -1], [0, 1], [1, -1], [1, 0], [1, 1]]))
+      @test point_matrix(boundary_lattice_points(square)) == _oscar_matrix_from_property(ZZ, boundary_lattice_points(square))
     if T == QQFieldElem
       @test is_smooth(Q0)
       @test is_normal(Q0)
@@ -111,8 +103,8 @@
     @test rays(RayVector, Pos) isa SubObjectIterator{RayVector{T}}
     @test rays(Pos) isa SubObjectIterator{RayVector{T}}
     @test length(rays(Pos)) == 3
-    @test vector_matrix(rays(Pos)) isa MatElem{T}
     @test issetequal(rays(Pos), ray_vector.(Ref(f), [[1, 0, 0], [0, 1, 0], [0, 0, 1]]))
+    @test vector_matrix(rays(Pos)) == _oscar_matrix_from_property(f, rays(Pos))
     @test lineality_space(L) isa SubObjectIterator{RayVector{T}}
     @test generator_matrix(lineality_space(L)) == matrix(f, [0 0 1])
     if T == QQFieldElem
@@ -151,7 +143,7 @@
     v = vertices(minkowski_sum(Q0, square))
     @test length(v) == 5
     @test issetequal(v, point_vector.(Ref(f), [[2, -1], [2, 1], [-1, -1], [-1, 2], [1, 2]]))
-    @test point_matrix(v) isa MatElem{T}
+    @test point_matrix(v) == _oscar_matrix_from_property(f, v)
     let S = Pair{Matrix{T},T}
       @test issetequal(facets(S, Pos), S.([f.([-1 0 0]), f.([0 -1 0]), f.([0 0 -1])], [f(0)]))
     end
@@ -190,13 +182,11 @@
     @test facets(Pos) isa SubObjectIterator{AffineHalfspace{T}}
     @test facets(Halfspace, Pos) isa SubObjectIterator{AffineHalfspace{T}}
     @test affine_hull(point) isa SubObjectIterator{AffineHyperplane{T}}
-    @test affine_equation_matrix(affine_hull(point)) isa MatElem{T}
-    @test size(affine_equation_matrix(affine_hull(point))) == (3, 4)
-    @test Oscar.affine_matrix_for_polymake(affine_hull(point)) isa Polymake.Matrix{Oscar._scalar_type_to_polymake(T)}
-    @test size(Oscar.affine_matrix_for_polymake(affine_hull(point))) == (3, 4)
     @test length(affine_hull(point)) == 3
     @test issetequal(affine_hull(point),
                      [hyperplane(f, [1 0 0], 0), hyperplane(f, [0 1 0], 1), hyperplane(f, [0 0 1], 0)])
+    @test affine_equation_matrix(affine_hull(point)) == _oscar_matrix_from_property(f, affine_hull(point))
+    @test Oscar.affine_matrix_for_polymake(affine_hull(point)) == _polymake_matrix_from_property(affine_hull(point))
     @test n_facets(square) == 4
     @test lineality_dim(Q0) == 0
     @test n_rays(Q1) == 1