diff --git a/src/elements.jl b/src/elements.jl
index 31f2bef6..d14de3c7 100644
--- a/src/elements.jl
+++ b/src/elements.jl
@@ -341,6 +341,20 @@ end
 lift(v::VStruct{T}) where {T} = constructor(v)(pushbefore(v.a, zero(T)))
 lift(v::AbstractVector{T}) where {T} = pushbefore(v, one(T))
 
+function MA.promote_operation(
+    ::typeof(translate),
+    ::Type{V},
+    ::Type{<:AbstractVector{T}},
+) where {S,V<:AbstractVector{S},T}
+    return similar_type(V, MA.promote_operation(+, S, T))
+end
+function MA.mutable_operate!(
+    ::typeof(translate),
+    a::AbstractVector,
+    b::AbstractVector,
+)
+    return MA.mutable_operate!(+, a, b)
+end
 translate(p::AbstractVector, v) = p + v
 translate(r::VStruct, v) = r
 
diff --git a/src/repelemop.jl b/src/repelemop.jl
index 8049d900..35ad3381 100644
--- a/src/repelemop.jl
+++ b/src/repelemop.jl
@@ -18,14 +18,14 @@ export translate
 function htranslate(p::HRep{T}, v::Union{AbstractVector{S}}) where {S, T}
     f = (i, h) -> translate(h, v)
     d = FullDim(p)
-    Tout = Base.promote_op(+, T, S)
+    Tout = MA.promote_operation(+, T, S)
     similar(p, d, Tout, hmap(f, d, Tout, p)...)
 end
 
 function vtranslate(p::VRep{T}, v::Union{AbstractVector{S}}) where {S, T}
     f = (i, u) -> translate(u, v)
     d = FullDim(p)
-    Tout = Base.promote_op(+, T, S)
+    Tout = MA.promote_operation(+, T, S)
     similar(p, d, Tout, vmap(f, d, Tout, p)...)
 end
 
@@ -54,6 +54,32 @@ function translate(p::Polyhedron, v)
     end
 end
 
+function MA.promote_operation(
+    ::typeof(translate),
+    P::Type{<:Rep{S}},
+    ::Type{<:AbstractVector{T}},
+) where {S,T}
+    U = MA.promote_operation(+, S, T)
+    return similar_type(P, U)
+end
+function MA.mutable_operate!(::typeof(translate), rep::VRepresentation, v)
+    return mutable_operate_elements!(translate, rep, v)
+end
+function MA.mutable_operate!(::typeof(translate), rep::HRepresentation, v)
+    return mutable_operate_elements!(translate, rep, v)
+end
+function MA.mutable_operate!(::typeof(translate), p::Polyhedron, v)
+    # The redundancy should not change with translation so we give
+    # the current redundancy information.
+    if hrepiscomputed(p)
+        sethrep!(MA.operate!(translate, hrep(p), v), hredundancy(p))
+    end
+    if vrepiscomputed(p)
+        # The redundancy should not change with translation
+        setvrep!(MA.operate!(translate, vrep(p), v), vredundancy(p))
+    end
+end
+
 ######
 # IN #
 ######
diff --git a/src/vecrep.jl b/src/vecrep.jl
index 499f9aae..3b43896e 100644
--- a/src/vecrep.jl
+++ b/src/vecrep.jl
@@ -180,6 +180,18 @@ convexhull!(v::PointsHull, p::AbstractVector) = push!(v.points, p)
 
 @vecrepelem PointsHull Point points
 
+MA.mutability(::Type{<:PointsHull}) = MA.IsMutable()
+function mutable_operate_elements!(
+    op::F,
+    v::PointsHull,
+    args::Vararg{Any,N},
+) where {F<:Function,N}
+    for i in eachindex(v.points)
+        v.points[i] = MA.operate!(op, v.points[i], args...)
+    end
+    return v
+end
+
 """
     vrep(lines::LineIt, rays::RayIt; d::FullDim)
 
@@ -233,6 +245,25 @@ convexhull!(v::RaysHull, r::Ray) = push!(v.rays, r)
 @vecrepelem RaysHull Ray rays
 @subrepelem RaysHull Line lines
 
+MA.mutability(::Type{<:RaysHull}) = MA.IsMutable()
+function mutable_operate_elements!(
+    ::typeof(translate),
+    ::RaysHull,
+    ::AbstractVector,
+)
+end
+function mutable_operate_elements!(
+    op::F,
+    v::RaysHull,
+    args::Vararg{Any,N},
+) where {F<:Function,N}
+    mutable_operate_elements!(op, v.lines, args...)
+    for i in eachindex(v.rays)
+        v.rays[i] = MA.operate!(op, v.rays[i], args...)
+    end
+    return v
+end
+
 vreptype(::Type{RaysHull{T, AT, D}}) where {T, AT, D} = Hull{T, AT, D}
 
 """
@@ -279,6 +310,17 @@ convexhull!(v::Hull, r::VStruct) = convexhull!(v.rays, r)
 @subrepelem Hull Line rays
 @subrepelem Hull Ray rays
 
+MA.mutability(::Type{<:Hull}) = MA.IsMutable()
+function mutable_operate_elements!(
+    op::F,
+    v::Hull,
+    args::Vararg{Any,N},
+) where {F<:Function,N}
+    mutable_operate_elements!(op, v.points, args...)
+    mutable_operate_elements!(op, v.rays, args...)
+    return v
+end
+
 fulltype(::Type{<:Union{Hull{T, AT, D}, PointsHull{T, AT, D}, LinesHull{T, AT, D}, RaysHull{T, AT, D}}}) where {T, AT, D} = Hull{T, AT, D}
 
 dualtype(::Type{<:Intersection{T, BT, D}}, ::Type{AT}) where {T, AT, BT, D} = Hull{T, AT, D}
diff --git a/test/repelemop.jl b/test/repelemop.jl
new file mode 100644
index 00000000..f52f7434
--- /dev/null
+++ b/test/repelemop.jl
@@ -0,0 +1,43 @@
+using Test
+
+import MutableArithmetics
+const MA = MutableArithmetics
+
+using Polyhedra
+
+function translate_test(T::Type)
+    o = one(T)
+    v = [o, -o]
+    # We need to create independent copies of `o` in case these are `BigInt`.
+    pr = convexhull([1o, 2o])
+    @test MA.promote_operation(translate, typeof(pr), typeof(v)) == typeof(pr)
+    @test MA.mutability(typeof(pr)) isa MA.IsMutable
+    @test MA.mutability(typeof(pr), translate, typeof(pr), typeof(v)) isa MA.IsMutable
+    rr = conichull([3o, -o])
+    @test MA.promote_operation(translate, typeof(rr), typeof(v)) == typeof(rr)
+    @test MA.mutability(typeof(rr)) isa MA.IsMutable
+    @test MA.mutability(typeof(rr), translate, typeof(rr), typeof(v)) isa MA.IsMutable
+    vr = pr + rr
+    @test MA.promote_operation(translate, typeof(vr), typeof(v)) == typeof(vr)
+    alloc_test(() -> MA.promote_operation(translate, typeof(vr), typeof(v)), 0)
+    @test MA.mutability(typeof(vr)) isa MA.IsMutable
+    @test MA.mutability(typeof(vr), translate, typeof(vr), typeof(v)) isa MA.IsMutable
+    alloc_test(() -> MA.mutability(typeof(vr), translate, typeof(vr), typeof(v)), 0)
+    vr2 = MA.operate!(translate, vr, v)
+    rec_identical(vr, vr2)
+    alloc_test(() -> MA.mutable_operate!(+, a, b), 0)
+    alloc_test(() -> MA.mutable_operate!(translate, a, b), 0)
+    alloc_test(() -> MA.mutable_operate!(translate, vr.points.points[1], v), 0)
+    alloc_test(() -> MA.mutable_operate!(translate, vr.points, v), 0)
+    alloc_test(() -> MA.mutable_operate!(translate, vr.rays, v), 0)
+    alloc_test(() -> MA.mutable_operate!(translate, vr, v), 0)
+    alloc_test(() -> MA.operate!(translate, vr, v), 0)
+
+#    hr = HalfSpace([1o, 1], 2o) ∩ HyperPlane([-o, 2o, 0o])
+#    @test MA.promote_operation(translate, typeof(hr), typeof(v)) == typeof(vr)
+#    @test MA.mutability(translate, typeof(hr), typeof(v)) isa MA.IsMutable
+end
+
+@testset "Translate" begin
+    translate_test(Float64)
+end
diff --git a/test/utils.jl b/test/utils.jl
index 5667d213..b06061c0 100644
--- a/test/utils.jl
+++ b/test/utils.jl
@@ -1,6 +1,35 @@
 using Test
 using Polyhedra
 
+# Allocating size for allocating a `BigInt`.
+# Half size on 32-bit.
+const BIGINT_ALLOC = Sys.WORD_SIZE == 64 ? 48 : 24
+
+function alloc_test(f, n)
+    f() # compile
+    @test n == @allocated f()
+end
+
+function rec_identical(vr::Polyhedra.LinesHull, vr2::Polyhedra.LinesHull)
+    @test vr === vr2
+    @test vr.lines === vr2.lines
+end
+function rec_identical(vr::Polyhedra.RaysHull, vr2::Polyhedra.RaysHull)
+    @test vr === vr2
+    @test vr2.rays === vr.rays
+    rec_identical(vr.lines, vr2.lines)
+end
+function rec_identical(vr::Polyhedra.PointsHull, vr2::Polyhedra.PointsHull)
+    @test vr === vr2
+    @test vr2.points === vr.points
+end
+
+function rec_identical(vr::Polyhedra.Hull, vr2::Polyhedra.Hull)
+    @test vr2 === vr
+    rec_identical(vr.points, vr2.points)
+    rec_identical(vr.rays, vr2.rays)
+end
+
 _isapprox(x::Real, y::Real) = _isapprox(promote(x, y)...)
 _isapprox(x::T, y::T) where {T<:Real} = x == y
 _isapprox(x::T, y::T) where {T<:AbstractFloat} = y < x+1024*eps(T) && x < y+1024*eps(T)