diff --git a/src/Grassmann.jl b/src/Grassmann.jl
index 5f8271d..d529ac8 100644
--- a/src/Grassmann.jl
+++ b/src/Grassmann.jl
@@ -601,12 +601,12 @@ function __init__()
     @require GeometryBasics = "5c1252a2-5f33-56bf-86c9-59e7332b4326" begin
         GeometryBasics.Point(t::Values) = GeometryBasics.Point(Tuple(t.v))
         GeometryBasics.Point(t::Variables) = GeometryBasics.Point(Tuple(t.v))
-        Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorTerm{V} where V = GeometryBasics.Point(value(Chain{V,valuetype(t)}(vector(t))))
+        Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorTerm{V} where V = convert(GeometryBasis.Point,Chain(t))
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorTerm{V,0} where V = GeometryBasics.Point(zeros(valuetype(t),mdims(V))...)
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:TensorAlgebra = GeometryBasics.Point(value(vector(t)))
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:Couple = GeometryBasics.Point(t.v.re,t.v.im)
         Base.convert(::Type{GeometryBasics.Point},t::T) where T<:Phasor = GeometryBasics.Point(t.v.re,t.v.im)
-        Base.convert(::Type{GeometryBasics.Point},t::Chain{V,G,T}) where {V,G,T} = G == 1 ? GeometryBasics.Point(value(vector(t))) : GeometryBasics.Point(zeros(T,mdims(V))...)
+        Base.convert(::Type{GeometryBasics.Point},t::Chain{V,G,T}) where {V,G,T} = GeometryBasics.Point(value(t))
         GeometryBasics.Point(t::T) where T<:TensorAlgebra = convert(GeometryBasics.Point,t)
         pointpair(p,V) = Pair(GeometryBasics.Point.(V.(value(p)))...)
         @pure ptype(::GeometryBasics.Point{N,T} where N) where T = T
diff --git a/src/composite.jl b/src/composite.jl
index ca2e56c..c227ceb 100644
--- a/src/composite.jl
+++ b/src/composite.jl
@@ -909,10 +909,10 @@ function Base.findlast(P,t::ChainBundle)
 end
 Base.findall(P,t) = findall(P .∈ getindex.(points(t),value(t)))
 
-edgelength(e) = (v=points(e)[value(e)]; value(abs(v[2]-v[1])))
-volumes(m,dets) = value.(abs.(.⋆(dets)))
-volumes(m) = mdims(Manifold(m))≠2 ? volumes(m,detsimplex(m)) : edgelength.(value(m))
-detsimplex(m::Vector{<:Chain{V}}) where V = ∧(m)/factorial(mdims(V)-1)
+edgelength(e) = (v=points(e)[value(e)]; Real(abs(v[2]-v[1])))
+volumes(m,dets) = Real.(abs.(dets))
+volumes(m) = mdims(Manifold(m))≠2 ? Real.(abs.(detsimplex(m))) : edgelength.(value(m))
+detsimplex(m::Vector{<:Chain{V}}) where V = det(m)/factorial(mdims(V)-1)
 detsimplex(m::ChainBundle) = detsimplex(value(m))
 mean(m::T) where T<:AbstractVector{<:Chain} = sum(m)/length(m)
 mean(m::T) where T<:Values = sum(m)/length(m)
@@ -923,9 +923,9 @@ barycenter(m::Chain{V,1,<:Chain} where V) = barycenter(value(m))
 curl(m::FixedVector{N,<:Chain{V}} where N) where V = curl(Chain{V,1}(m))
 curl(m::Values{N,<:Chain{V}} where N) where V = curl(Chain{V,1}(m))
 curl(m::T) where T<:TensorAlgebra = Manifold(m)(∇)×m
-LinearAlgebra.det(t::Chain{V,1,<:Chain} where V) = ∧(t)
-LinearAlgebra.det(m::Vector{<:Chain{V}}) where V = ∧(m)
-LinearAlgebra.det(m::ChainBundle) = ∧(m)
+LinearAlgebra.det(t::Chain{V,1,<:Chain} where V) = !∧(t)
+LinearAlgebra.det(m::Vector{<:Chain{V}}) where V = .!∧(m)
+LinearAlgebra.det(m::ChainBundle) = .!∧(m)
 ∧(m::ChainBundle) = ∧(value(m))
 function ∧(m::Vector{<:Chain{V}}) where V
     p = points(m); pm = p[m]
diff --git a/src/forms.jl b/src/forms.jl
index e63c748..c0c511c 100644
--- a/src/forms.jl
+++ b/src/forms.jl
@@ -487,8 +487,10 @@ Base.zero(t::Type{<:DiagonalOperator{V,T}}) where {V,T} = DiagonalOperator(zero(
 
 scalar(m::DiagonalOperator) = tr(m)/length(value(m))
 LinearAlgebra.tr(m::DiagonalOperator) = sum(value(value(m)))
-LinearAlgebra.det(m::DiagonalMorphism{V}) where V = Chain{V,mdims(V)}(prod(value(value(m))))
-LinearAlgebra.det(m::DiagonalOutermorphism{V}) where V = value(m)(Val(mdims(V)))
+LinearAlgebra.det(m::DiagonalMorphism) = !∧(m)
+LinearAlgebra.det(m::DiagonalOutermorphism) = !∧(m)
+∧(m::DiagonalMorphism{V}) where V = Chain{V,mdims(V)}(prod(value(value(m))))
+∧(m::DiagonalOutermorphism{V}) where V = value(m)(Val(mdims(V)))
 compound(m::DiagonalMorphism{V},::Val{0}) where V = DiagonalOperator(Chain{V,0}(1))
 @generated function compound(m::DiagonalMorphism{V},::Val{G}) where {V,G}
     Expr(:call,:DiagonalOperator,Expr(:call,:(Chain{V,G}),Expr(:call,Values,[Expr(:call,:*,[:(@inbounds m.v[$i]) for i ∈ indices(j)]...) for j ∈ indexbasis(mdims(V),G)]...)))
@@ -551,7 +553,8 @@ getindex(t::TensorOperator,i::Int) = value(t.v)[i]
 Base.transpose(t::TensorOperator) = TensorOperator(transpose(value(t)))
 scalar(m::Endomorphism) = tr(m)/length(value(m))
 LinearAlgebra.tr(m::Endomorphism) = tr(value(m))
-LinearAlgebra.det(t::TensorOperator) = ∧(value(t))
+LinearAlgebra.det(t::TensorOperator) = !∧(value(t))
+∧(t::TensorOperator) = ∧(value(t))
 
 Base.zero(t::TensorOperator) = TensorOperator(zero(value(t)))
 Base.zero(t::Type{<:TensorOperator{V,W,T}}) where {V,W,T} = TensorOperator(zero(T))
@@ -676,7 +679,8 @@ getindex(t::Outermorphism{V},i::Int) where V = iszero(i) ? Chain{V,0}((Chain(One
 Base.transpose(m::Outermorphism) = Outermorphism(map(transpose,value(m)))
 scalar(m::Outermorphism{V}) where V = tr(m)/(1<<mdims(V))
 LinearAlgebra.tr(m::Outermorphism) = 1+sum(map(tr,value(m)))
-LinearAlgebra.det(m::Outermorphism) = (@inbounds value(value(m)[end])[1])
+LinearAlgebra.det(m::Outermorphism) = !∧(m)
+∧(m::Outermorphism) = (@inbounds value(value(m)[end])[1])
 
 Base.zero(t::Outermorphism) = Outermorphism(zero.(value(t)))
 @generated function Base.zero(t::Type{<:Outermorphism{V,T}}) where {V,T}
@@ -1156,7 +1160,7 @@ eigpolys(X::DiagonalOutermorphism) = eigpolys(value(X)(Val(1)))
 
 eigprods(X,G::Int) = eigprods(X,Val(G))
 eigprods(X::TensorNested) = eigprods(eigvalsreal(X))
-eigprods(X::TensorNested{V},g::Val{G}) where {V,G} = mdims(V)≠G ? eigprods(eigvalsreal(X),g) : det(X)
+eigprods(X::TensorNested{V},g::Val{G}) where {V,G} = mdims(V)≠G ? eigprods(eigvalsreal(X),g) : ∧(X)
 eigprods(X::TensorAlgebra{V},::Val{0}) where V = Chain{V,0}(1)
 eigprods(x::Chain{V,1} where V,::Val{1}) = x
 @generated function eigprods(x::Chain{V,1},::Val{G}) where {V,G}