diff --git a/src/flat.jl b/src/flat.jl
index af405a4..4390d06 100644
--- a/src/flat.jl
+++ b/src/flat.jl
@@ -6,9 +6,13 @@ end
 SemialgebraicSets.is_zero_dimensional(::ZeroDimensionalVariety) = true
 Base.length(v::ZeroDimensionalVariety) = length(v.elements)
 Base.iterate(v::ZeroDimensionalVariety, args...) = iterate(v.elements, args...)
-function Base.show(io::IO, V::ZeroDimensionalVariety)
+function Base.show(io::IO, ::MIME"text/plain", V::ZeroDimensionalVariety)
     println(io, "ZeroDimensionalVariety with elements:")
-    return show(io, V.elements)
+    show(io, V.elements)
+    return
+end
+function Base.show(io::IO, V::ZeroDimensionalVariety)
+    return show(io, MIME"text/plain"(), V)
 end
 
 # Decomposition of the pencil of matrices
diff --git a/src/null.jl b/src/null.jl
index ac4e684..a76faf8 100644
--- a/src/null.jl
+++ b/src/null.jl
@@ -32,6 +32,17 @@ function Base.getindex(
     )
 end
 
+function MacaulayNullspace(
+    ν::MomentMatrix,
+    rank_check::RankCheck,
+    ldlt::LowRankLDLTAlgorithm = SVDLDLT(),
+)
+    M = value_matrix(ν)
+    chol = low_rank_ldlt(M, ldlt, rank_check)
+    @assert size(chol.L, 1) == LinearAlgebra.checksquare(M)
+    return MacaulayNullspace(chol.L, ν.basis, accuracy(chol))
+end
+
 abstract type MacaulayNullspaceSolver end
 
 function solve(null::MacaulayNullspace, solver::MacaulayNullspaceSolver)
@@ -58,11 +69,8 @@ function compute_support!(
     rank_check::RankCheck,
     solver::ImageSpaceSolver,
 )
-    M = value_matrix(ν)
-    chol = low_rank_ldlt(M, solver.ldlt, rank_check)
-    @assert size(chol.L, 1) == LinearAlgebra.checksquare(M)
     ν.support =
-        solve(MacaulayNullspace(chol.L, ν.basis, accuracy(chol)), solver.null)
+        solve(MacaulayNullspace(ν, rank_check, solver.ldlt), solver.null)
     return
 end
 
diff --git a/test/commutativetests.jl b/test/commutativetests.jl
index 47a6b9b..42c459a 100644
--- a/test/commutativetests.jl
+++ b/test/commutativetests.jl
@@ -2,6 +2,7 @@ include("moment_vector.jl")
 include("expectation.jl")
 include("moment_matrix.jl")
 include("rank.jl")
+include("flat.jl")
 include("extract.jl")
 include("atomic.jl")
 include("hermitian_poly.jl")
diff --git a/test/flat.jl b/test/flat.jl
new file mode 100644
index 0000000..aa84ae8
--- /dev/null
+++ b/test/flat.jl
@@ -0,0 +1,8 @@
+using Test, MultivariateMoments
+
+@testset "ZeroDimensionalVariety" begin
+    V = ZeroDimensionalVariety([[1], [2]])
+    expected = "ZeroDimensionalVariety with elements:\n[[1], [2]]"
+    @test sprint(show, V) == expected
+    @test sprint(show, MIME"text/plain"(), V) == expected
+end