diff --git a/.appveyor.yml b/.appveyor.yml
index 855eaa7..94fe534 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -2,10 +2,8 @@ environment:
   matrix:
   - julia_version: 1
   - julia_version: 1.6
-  - julia_version: 1.7
-  - julia_version: 1.8
-  - julia_version: 1.9
   - julia_version: 1.10
+  - julia_version: 1.11
   - julia_version: nightly
 
 platform:
diff --git a/src/algebra.jl b/src/algebra.jl
index cd030a4..4140a29 100644
--- a/src/algebra.jl
+++ b/src/algebra.jl
@@ -13,13 +13,16 @@
 #   https://crucialflow.com
 
 import Base: +, -, *, ^, /, //, inv, <, >, <<, >>, >>>
-import AbstractTensors: ∧, ∨, ⟑, ⊗, ⊛, ⊙, ⊠, ⨼, ⨽, ⋆, ∗, rem, div, TAG, SUB
+import AbstractTensors: ∧, ∨, ⟑, ⊖, ⊘, ⊗, ⊛, ⊙, ⊠, ⨼, ⨽, ⋆, ∗, rem, div, TAG, SUB
 import AbstractTensors: plus, minus, times, contraction, equal, wedgedot, veedot
 import AbstractTensors: pseudosandwich, antisandwich, antidot
 import Leibniz: diffcheck, diffmode, symmetricsplit
 import Leibniz: loworder, isnull, Field, ExprField
 const Sym,SymField = :AbstractTensors,Any
 
+export ∗, ⊛, ⊖, ∧, ∨, ⟑, wedgedot, veedot, ⊗, ⨼, ⨽, ⊙, ⊠, ⟂, ∥
+export ⊘, sandwich, pseudosandwich, antisandwich
+
 if VERSION >= v"1.10.0"; @eval begin
     import AbstractTensors.$(Symbol("⟇"))
     export $(Symbol("⟇"))
@@ -89,9 +92,6 @@ function wedgedot_metric(a::Submanifold{V},b::Single{V},g) where V
     order(b.v)+order(bas)>diffmode(V) ? Zero(V) : v*bas
 end
 
-export ∗, ⊛, ⊖
-import AbstractTensors: ⊖, ⊘, ∗
-
 @doc """
     ∗(ω::TensorAlgebra,η::TensorAlgebra)
 
@@ -139,8 +139,6 @@ function ∧(a::X,b::Y) where {X<:TensorTerm{V},Y<:TensorTerm{V}} where V
     return Single{V}(parity(x,y) ? -v : v,getbasis(V,(A⊻B)|Q))
 end
 
-export ∧, ∨, ⟑, wedgedot, veedot, ⊗
-
 #⊗(a::A,b::B) where {A<:TensorAlgebra,B<:TensorAlgebra} = a∧b
 ⊗(a::A,b::B) where {A<:TensorGraded,B<:TensorGraded} = Dyadic(a,b)
 ⊗(a::A,b::B) where {A<:TensorGraded,B<:TensorGraded{V,0} where V} = a*b
@@ -196,9 +194,6 @@ Regressive product as defined by the DeMorgan's law: ∨(ω...) = ⋆⁻¹(∧(
 
 ## interior product: a ∨ ⋆(b)
 
-import LinearAlgebra: dot, ⋅
-export ⋅
-
 """
     contraction(ω::TensorAlgebra,η::TensorAlgebra)
 
@@ -268,8 +263,6 @@ end
     end
 end
 
-export ⨼, ⨽
-
 @doc """
     dot(ω::TensorAlgebra,η::TensorAlgebra)
 
@@ -278,9 +271,6 @@ Interior (right) contraction product: ω⋅η = ω∨⋆η
 
 ## cross product
 
-import LinearAlgebra: cross, ×
-export ×
-
 @doc """
     cross(ω::TensorAlgebra,η::TensorAlgebra)
 
@@ -289,8 +279,6 @@ Cross product: ω×η = ⋆(ω∧η)
 
 # symmetrization and anti-symmetrization
 
-export ⊙, ⊠
-
 """
     ⊙(ω::TensorAlgebra,η::TensorAlgebra)
 
@@ -315,14 +303,12 @@ end
 
 ## sandwich product
 
-export ⊘, sandwich, pseudosandwich, antisandwich
-
 ⊘(x::TensorTerm{V},y::TensorTerm{V}) where V = reverse(y)*x*involute(y)
 ⊘(x::TensorAlgebra{V},y::TensorAlgebra{V}) where V = reverse(y)*x*involute(y)
 ⊘(x::Couple{V},y::TensorAlgebra{V}) where V = (scalar(x)⊘y)+(imaginary(x)⊘y)
 ⊘(x::PseudoCouple{V},y::TensorAlgebra{V}) where V = (imaginary(x)⊘y)+(volume(x)⊘y)
 @generated ⊘(a::TensorGraded{V,G},b::Spinor{V}) where {V,G} = product_sandwich(a,b)
-@generated ⊘(a::TensorGraded{V,G},b::AntiSpinor{V}) where {V,G} = product_sandwich(a,b)
+@generated ⊘(a::TensorGraded{V,G},b::CoSpinor{V}) where {V,G} = product_sandwich(a,b)
 @generated ⊘(a::TensorGraded{V,G},b::Couple{V}) where {V,G} = product_sandwich(a,b)
 @generated ⊘(a::TensorGraded{V,G},b::PseudoCouple{V}) where {V,G} = product_sandwich(a,b)
 @generated ⊘(a::TensorGraded{V,G},b::TensorGraded{V,L}) where {V,G,L} = product_sandwich(a,b)
@@ -330,7 +316,7 @@ export ⊘, sandwich, pseudosandwich, antisandwich
     isinduced(g) && (return :(a⊘b))
     product_sandwich(a,b,false,true)
 end
-@generated function ⊘(a::TensorGraded{V,G},b::AntiSpinor{V},g) where {V,G}
+@generated function ⊘(a::TensorGraded{V,G},b::CoSpinor{V},g) where {V,G}
     isinduced(g) && (return :(a⊘b))
     product_sandwich(a,b,false,true)
 end
@@ -360,7 +346,7 @@ For normalized even grade η it is ω⊘η = (~η)⊖ω⊖η
 >>>(y::TensorAlgebra{V},x::Couple{V}) where V = (y>>>scalar(x))+(y>>>imaginary(x))
 >>>(y::TensorAlgebra{V},x::PseudoCouple{V}) where V = (y>>>imaginary(x))+(y>>>volume(x))
 @generated >>>(b::Spinor{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
-@generated >>>(b::AntiSpinor{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
+@generated >>>(b::CoSpinor{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
 @generated >>>(b::Couple{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
 @generated >>>(b::PseudoCouple{V},a::TensorGraded{V,G}) where {V,G} = product_sandwich(a,b,true)
 @generated >>>(b::TensorGraded{V,L},a::TensorGraded{V,G}) where {V,G,L} = product_sandwich(a,b,true)
@@ -368,7 +354,7 @@ For normalized even grade η it is ω⊘η = (~η)⊖ω⊖η
     isinduced(g) && (return :(b>>>a))
     product_sandwich(a,b,true,true)
 end
-@generated function >>>(b::AntiSpinor{V},a::TensorGraded{V,G},g) where {V,G}
+@generated function >>>(b::CoSpinor{V},a::TensorGraded{V,G},g) where {V,G}
     isinduced(g) && (return :(b>>>a))
     product_sandwich(a,b,true,true)
 end
@@ -405,8 +391,6 @@ antidot_metric(a,b) = complementleft(contraction_metric(complementright(a),compl
 
 ## linear algebra
 
-export ⟂, ∥
-
 ∥(a,b) = iszero(a∧b)
 
 ## exponentiation
@@ -511,7 +495,7 @@ for (nv,d) ∈ ((:inv,:/),(:inv_rat,://))
             throw(error("inv($m) is undefined"))
         end
     end
-    for pinor ∈ (:Spinor,:AntiSpinor)
+    for pinor ∈ (:Spinor,:CoSpinor)
         @eval begin
             function $nv(m::$pinor{V,T},$(args...)) where {V,T}
                 rm = ~m
@@ -800,7 +784,7 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
         end end
     end
     @noinline function adderanti(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
-        (iseven(L) || iseven(G)) && (return :(error("$(basis(a)) and $(basis(b)) are not expressible as AntiSpinor")))
+        (iseven(L) || iseven(G)) && (return :(error("$(basis(a)) and $(basis(b)) are not expressible as CoSpinor")))
         left,bop,VEC = addvec(a,b,false,op)
         if mdims(V)-1<cache_limit
             $(insert_expr((:N,),:svecs)...)
@@ -808,13 +792,13 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
             out,ib = svecs(N,Any)(zeros(svecs(N,t<:Number ? t : Int))),indexbasis(N)
             setanti!_pre(out,:(value(a,$t)),UInt(basis(a)),Val{N}())
             setanti!_pre(out,:($bop(value(b,$t))),UInt(basis(b)),Val{N}())
-            return :(AntiSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
+            return :(CoSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
         else quote
             $(insert_expr((:N,:t),VEC)...)
             out = zeros(mvecs(N,t))
             setanti!(out,value(a,t),UInt(basis(a)),Val{N}())
             setanti!(out,$bop(value(b,t)),UInt(basis(b)),Val{N}())
-            return AntiSpinor{V}(out)
+            return CoSpinor{V}(out)
         end end
     end
     @noinline function addermulti(a::Type{<:TensorTerm{V,L}},b::Type{<:TensorTerm{V,G}},op) where {V,L,G}
@@ -918,17 +902,17 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
                 end
                 val = :(@inbounds $left(value(a,$t)))
                 setanti!_pre(out,val,X,Val(N))
-                return :(AntiSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
+                return :(CoSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
             else return if !swap; quote
                 $(insert_expr((:N,:t,:out,:rrr,:bng),VECS)...)
                 @inbounds out[rrr+1:rrr+bng] = $(bcast(right,:(value(b,$VEC(N,G,t)),)))
                 addpseudo(out,value(a,t),UInt(basis(a)),Val(N))
-                return AntiSpinor{V}(out)
+                return CoSpinor{V}(out)
             end; else quote
                 $(insert_expr((:N,:t,:out,:rrr,:bng),VECS)...)
                 @inbounds out[rrr+1:rrr+bng] = value(a,$VEC(N,G,t))
                 addanti!(out,$left(value(b,t)),UInt(basis(b)),Val(N))
-                return AntiSpinor{V}(out)
+                return CoSpinor{V}(out)
             end end end
         else
             if mdims(V)<cache_limit
@@ -1015,7 +999,7 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
             return Spinor{V}(out)
         end end end
     end
-    @noinline function adder(a::Type{<:TensorTerm{V,G}},b::Type{<:AntiSpinor{V,T}},op,swap=false) where {V,G,T}
+    @noinline function adder(a::Type{<:TensorTerm{V,G}},b::Type{<:CoSpinor{V,T}},op,swap=false) where {V,G,T}
         left,right,VEC = addvec(a,b,swap,op)
         VECS = Symbol(string(VEC)*"s")
         !isodd(G) && (return swap ? :($op(Multivector(b),a)) : :($op(a,Multivector(b))))
@@ -1032,24 +1016,24 @@ adder(a,b,op=:+) = adder(typeof(a),typeof(b),op)
                     setanti!_pre(out,val,B,Val(N))
                 end
             end
-            return :(AntiSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
+            return :(CoSpinor{V}($(Expr(:call,tvecs(N,t<:Number ? t : Any),out...))))
         else return if !swap; quote
             $(insert_expr((:N,:t),VEC)...)
             out = convert($VECS(N,t),$(bcast(right,:(value(b,$VECS(N,t)),))))
             addanti!(out,value(a,t),UInt(basis(a)),Val(N))
-            return AntiSpinor{V}(out)
+            return CoSpinor{V}(out)
         end; else quote
             $(insert_expr((:N,:t),VEC)...)
             out = value(a,$VECS(N,t))
             addpseudo(out,$left(value(b,t)),UInt(basis(b)),Val(N))
-            return AntiSpinor{V}(out)
+            return CoSpinor{V}(out)
         end end end
     end
     @noinline function product(a::Type{S},b::Type{<:Chain{V,G,T}},swap=false,field=false) where S<:TensorGraded{V,L} where {V,G,L,T}
         MUL,VEC = mulvecs(a,b)
         vfield = Val(field)
         anti = isodd(L) ≠ isodd(G)
-        type = anti ? :AntiSpinor : :Spinor
+        type = anti ? :CoSpinor : :Spinor
         args = field ? (:g,) : ()
         (S<:Zero || S<:Infinity) && (return :a)
         if G == 0
@@ -1341,13 +1325,13 @@ for (op,po,GL,grass) ∈ ((:∧,:>,:(G+L),:exter),(:∨,:<,:(G+L-mdims(V)),:meet
     end
 end
 
-for input ∈ (:Multivector,:Spinor,:AntiSpinor)
-    inspin,inanti = input==:Spinor,input==:AntiSpinor
+for input ∈ (:Multivector,:Spinor,:CoSpinor)
+    inspin,inanti = input==:Spinor,input==:CoSpinor
 for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
                      (:∨,:meetadd),(:contraction,:skewadd))
     outspin = product ∈ (:exteradd,:geomadd,:skewadd)
     outmulti = input == :Multivector
-    outype = outmulti ? :Multivector : outspin ? :($(inspin ? :isodd : :iseven)(G) ? AntiSpinor : Spinor) : inspin ?  :(isodd(G)⊻isodd(N) ? AntiSpinor : Spinor) : :(isodd(G)⊻isodd(N) ? Spinor : AntiSpinor)
+    outype = outmulti ? :Multivector : outspin ? :($(inspin ? :isodd : :iseven)(G) ? CoSpinor : Spinor) : inspin ?  :(isodd(G)⊻isodd(N) ? CoSpinor : Spinor) : :(isodd(G)⊻isodd(N) ? Spinor : CoSpinor)
     product! = outmulti ? Symbol(product,:multi!) : outspin ? :($(inspin ? :isodd : :iseven)(G) ? $(Symbol(product,:anti!)) : $(Symbol(product,:spin!))) : :(isodd(G)⊻isodd(N) ? $(Symbol(product,outspin⊻inspin ? :anti! : :spin!)) : $(Symbol(product,outspin⊻inspin ? :spin! : :anti!)))
     preproduct! = outmulti ? Symbol(product,:multi!_pre) : outspin ? :($(inspin ? :isodd : :iseven)(G) ? $(Symbol(product,:anti!_pre)) : $(Symbol(product,:spin!_pre))) : :(isodd(G)⊻isodd(N) ? $(Symbol(product,outspin⊻inspin ? :anti!_pre : :spin!_pre)) : $(Symbol(product,outspin⊻inspin ? :spin!_pre : :anti!_pre)))
     prop = op≠:* ? Symbol(:product_,op) : :product
@@ -1453,9 +1437,9 @@ for (op,product) ∈ ((:∧,:exteradd),(:*,:geomadd),
 end
 end
 
-for input ∈ (:Spinor,:AntiSpinor)
+for input ∈ (:Spinor,:CoSpinor)
     inspin = input==:Spinor
-    outype = :($(inspin ? :isodd : :iseven)(G) ? AntiSpinor : Spinor)
+    outype = :($(inspin ? :isodd : :iseven)(G) ? CoSpinor : Spinor)
     product! = :($(inspin ? :isodd : :iseven)(G) ? geomaddanti! : geomaddspin!)
     preproduct! = :($(inspin ? :isodd : :iseven)(G) ? geomaddanti!_pre : geomaddspin!_pre)
     product2! = :(isodd(G) ? geomaddanti! : geomaddspin!)
diff --git a/src/composite.jl b/src/composite.jl
index 3239f59..92acd57 100644
--- a/src/composite.jl
+++ b/src/composite.jl
@@ -15,6 +15,7 @@
 export exph, log_fast, logh_fast, pseudoexp, pseudolog, pseudometric, pseudodot, @pseudo
 export pseudoabs, pseudoabs2, pseudosqrt, pseudocbrt, pseudoinv, pseudoscalar
 export pseudocos, pseudosin, pseudotan, pseudocosh, pseudosinh, pseudotanh
+export vandermonde, volumes, detsimplex, submesh
 
 ## exponential & logarithm function
 
@@ -297,7 +298,7 @@ for (op,logm,field) ∈ ((:⟑,:(Base.log),false),(:wedgedot_metric,:log_metric,
     args = field ? (:g,) : ()
     indu(t=:(log(t))) = field ? :(isinduced(g) && (return :($$t))) : nothing
 @eval qlog(b::PseudoCouple,$(args...),x::Int=10000) = qlog(multispin(b),$(args...),x)
-@eval qlog(b::AntiSpinor,$(args...),x::Int=10000) = qlog(Multivector(b),$(args...),x)
+@eval qlog(b::CoSpinor,$(args...),x::Int=10000) = qlog(Multivector(b),$(args...),x)
 @eval function qlog(w::T,$(args...),x::Int=10000) where T<:TensorAlgebra
     $(indu(:(qlog(w,x))))
     V = Manifold(w)
@@ -319,7 +320,7 @@ for (op,logm,field) ∈ ((:⟑,:(Base.log),false),(:wedgedot_metric,:log_metric,
 end # http://www.netlib.org/cephes/qlibdoc.html#qlog
 
 @eval qlog_fast(b::PseudoCouple,$(args...),x::Int=10000) = qlog_fast(multispin(b),$(args...),x)
-@eval qlog_fast(b::AntiSpinor,$(args...),x::Int=10000) = qlog_fast(Multivector(b),$(args...),x)
+@eval qlog_fast(b::CoSpinor,$(args...),x::Int=10000) = qlog_fast(Multivector(b),$(args...),x)
 for pinor ∈ (:Multivector,:Spinor); VEC = pinor≠:Spinor ? :mvec : :mvecs
 @eval @generated function qlog_fast(b::$pinor{V,T,E},$(args...),x::Int=10000) where {V,T,E}
     $(indu(:(qlog_fast(b,x))))
@@ -387,17 +388,17 @@ end
 end
 
 @eval begin
-    Base.exp(t::AntiSpinor,$(args...)) = exp(Multivector(t),$(args...))
-    Base.expm1(t::AntiSpinor,$(args...)) = expm1(Multivector(t),$(args...))
-    $logm(t::AntiSpinor,$(args...)) = $logm(Multivector(t),$(args...))
-    Base.log1p(t::AntiSpinor,$(args...)) = log1p(Multivector(t),$(args...))
-    log_fast(t::AntiSpinor,$(args...)) = log_fast(Multivector(t),$(args...))
-    logh_fast(t::AntiSpinor,$(args...)) = logh_fast(Multivector(t),$(args...))
+    Base.exp(t::CoSpinor,$(args...)) = exp(Multivector(t),$(args...))
+    Base.expm1(t::CoSpinor,$(args...)) = expm1(Multivector(t),$(args...))
+    $logm(t::CoSpinor,$(args...)) = $logm(Multivector(t),$(args...))
+    Base.log1p(t::CoSpinor,$(args...)) = log1p(Multivector(t),$(args...))
+    log_fast(t::CoSpinor,$(args...)) = log_fast(Multivector(t),$(args...))
+    logh_fast(t::CoSpinor,$(args...)) = logh_fast(Multivector(t),$(args...))
 end
 for op ∈ (:cosh,:sinh)
     @eval begin
         Base.$op(t::PseudoCouple,$(args...)) = $op(multispin(t),$(args...))
-        Base.$op(t::AntiSpinor,$(args...)) = $op(Multivector(t),$(args...))
+        Base.$op(t::CoSpinor,$(args...)) = $op(Multivector(t),$(args...))
     end
 end
 
@@ -825,8 +826,6 @@ Base.in(v::Chain{V,1},t::Chain{W,1,<:Chain{V,1}}) where {V,W} = v ∈ value(t)
 Base.inv(t::Chain{V,1,<:Chain{W,1}}) where {W,V} = inv(value(t))
 grad(t::Chain{V,1,<:Chain{W,1}}) where {V,W} = grad(value(t))
 
-export vandermonde
-
 @generated approx(x,y::Chain{V}) where V = :(polynom(x,$(Val(mdims(V))))⋅y)
 approx(x,y::Values{N}) where N = value(polynom(x,Val(N)))⋅y
 approx(x,y::AbstractVector) = [x^i for i ∈ 0:length(y)-1]⋅y
@@ -906,8 +905,6 @@ function Base.findlast(P,t::ChainBundle)
 end
 Base.findall(P,t) = findall(P .∈ getindex.(points(t),value(t)))
 
-export volumes, detsimplex, submesh
-
 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))
@@ -1007,7 +1004,7 @@ for op ∈ (:div,:rem,:mod,:mod1,:fld,:fld1,:cld,:ldexp)
         Base.$op(a::PseudoCouple{V,B},m) where {V,B} = PseudoCouple{V,B}($op(value(a),m))
         Base.$op(a::Chain{V,G,T},m) where {V,G,T} = Chain{V,G}($op.(value(a),m))
         Base.$op(a::Spinor{V,T},m) where {T,V} = Spinor{V}($op.(value(a),m))
-        Base.$op(a::AntiSpinor{V,T},m) where {T,V} = AntiSpinor{V}($op.(value(a),m))
+        Base.$op(a::CoSpinor{V,T},m) where {T,V} = CoSpinor{V}($op.(value(a),m))
         Base.$op(a::Multivector{V,T},m) where {T,V} = Multivector{V}($op.(value(a),m))
     end
 end
@@ -1017,20 +1014,20 @@ for op ∈ (:mod2pi,:rem2pi,:rad2deg,:deg2rad,:round)
         Base.$op(a::PseudoCouple{V,B};args...) where {V,B} = PseudoCouple{V,B}($op(value(a);args...))
         Base.$op(a::Chain{V,G,T};args...) where {V,G,T} = Chain{V,G}($op.(value(a);args...))
         Base.$op(a::Spinor{V,T};args...) where {V,T} = Spinor{V}($op.(value(a);args...))
-        Base.$op(a::AntiSpinor{V,T};args...) where {V,T} = AntiSpinor{V}($op.(value(a);args...))
+        Base.$op(a::CoSpinor{V,T};args...) where {V,T} = CoSpinor{V}($op.(value(a);args...))
         Base.$op(a::Multivector{V,T};args...) where {V,T} = Multivector{V}($op.(alue(a);args...))
     end
 end
 Base.isfinite(a::Chain) = prod(isfinite.(value(a)))
 Base.isfinite(a::Spinor) = prod(isfinite.(value(a)))
-Base.isfinite(a::AntiSpinor) = prod(isfinite.(value(a)))
+Base.isfinite(a::CoSpinor) = prod(isfinite.(value(a)))
 Base.isfinite(a::Multivector) = prod(isfinite.(value(a)))
 Base.isfinite(a::Couple) = isfinite(value(a))
 Base.isfinite(a::PseudoCouple) = isfinite(value(a))
 Base.rationalize(t::Type,a::Chain{V,G,T};tol::Real=eps(T)) where {V,G,T} = Chain{V,G}(rationalize.(t,value(a),tol))
 Base.rationalize(t::Type,a::Multivector{V,T};tol::Real=eps(T)) where {V,T} = Multivector{V}(rationalize.(t,value(a),tol))
 Base.rationalize(t::Type,a::Spinor{V,T};tol::Real=eps(T)) where {V,T} = Spinor{V}(rationalize.(t,value(a),tol))
-Base.rationalize(t::Type,a::AntiSpinor{V,T};tol::Real=eps(T)) where {V,T} = AntiSpinor{V}(rationalize.(t,value(a),tol))
+Base.rationalize(t::Type,a::CoSpinor{V,T};tol::Real=eps(T)) where {V,T} = CoSpinor{V}(rationalize.(t,value(a),tol))
 Base.rationalize(t::Type,a::Couple{V,B};tol::Real=eps(T)) where {V,B} = Couple{V,B}(rationalize(t,value(a),tol))
 Base.rationalize(t::Type,a::PseudoCouple{V,B};tol::Real=eps(T)) where {V,B} = PseudoCouple{V,B}(rationalize(t,value(a),tol))
 Base.rationalize(t::T;kvs...) where T<:TensorAlgebra = rationalize(Int,t;kvs...)
@@ -1067,7 +1064,7 @@ end
 
 Base.map(fn, x::Multivector{V}) where V = Multivector{V}(map(fn, value(x)))
 Base.map(fn, x::Spinor{V}) where V = Spinor{V}(map(fn, value(x)))
-Base.map(fn, x::AntiSpinor{V}) where V = AntiSpinor{V}(map(fn, value(x)))
+Base.map(fn, x::CoSpinor{V}) where V = CoSpinor{V}(map(fn, value(x)))
 Base.map(fn, x::Chain{V,G}) where {V,G} = Chain{V,G}(map(fn,value(x)))
 Base.map(fn, x::TensorTerm) = fn(value(x))*basis(x)
 Base.map(fn, x::Couple{V,B}) where {V,B} = Couple{V,B}(Complex(fn(x.v.re),fn(x.v.im)))
@@ -1085,9 +1082,9 @@ Base.rand(::AbstractRNG,::SamplerType{Multivector{V,T}}) where {V,T} = Multivect
 Base.rand(::AbstractRNG,::SamplerType{Spinor}) = rand(Spinor{rand(Manifold)})
 Base.rand(::AbstractRNG,::SamplerType{Spinor{V}}) where V = Spinor{V}(DirectSum.orand(svecs(mdims(V),Float64)))
 Base.rand(::AbstractRNG,::SamplerType{Spinor{V,T}}) where {V,T} = Spinor{V}(rand(svecs(mdims(V),T)))
-Base.rand(::AbstractRNG,::SamplerType{AntiSpinor}) = rand(AntiSpinor{rand(Manifold)})
-Base.rand(::AbstractRNG,::SamplerType{AntiSpinor{V}}) where V = AntiSpinor{V}(DirectSum.orand(svecs(mdims(V),Float64)))
-Base.rand(::AbstractRNG,::SamplerType{AntiSpinor{V,T}}) where {V,T} = AntiSpinor{V}(rand(svecs(mdims(V),T)))
+Base.rand(::AbstractRNG,::SamplerType{CoSpinor}) = rand(CoSpinor{rand(Manifold)})
+Base.rand(::AbstractRNG,::SamplerType{CoSpinor{V}}) where V = CoSpinor{V}(DirectSum.orand(svecs(mdims(V),Float64)))
+Base.rand(::AbstractRNG,::SamplerType{CoSpinor{V,T}}) where {V,T} = CoSpinor{V}(rand(svecs(mdims(V),T)))
 Base.rand(::AbstractRNG,::SamplerType{Couple}) = rand(Couple{rand(Manifold)})
 Base.rand(::AbstractRNG,::SamplerType{Couple{V}}) where V = rand(Couple{V,Submanifold{V}(UInt(rand(1:1<<mdims(V)-1)))})
 Base.rand(::AbstractRNG,::SamplerType{Couple{V,B}}) where {V,B} = Couple{V,B}(rand(Complex{Float64}))
diff --git a/src/forms.jl b/src/forms.jl
index c3edf51..61b452e 100644
--- a/src/forms.jl
+++ b/src/forms.jl
@@ -1,6 +1,10 @@
 #   This file is part of Grassmann.jl. It is licensed under the AGPL license
 #   Grassmann Copyright (C) 2019 Michael Reed
 
+export TensorNested, Projector, Dyadic, Proj, outer, InducedMetric
+export DiagonalOperator, TensorOperator, Endomorphism, Outermorphism, outermorphism
+export operator, gradedoperator, evenoperator, oddoperator, MetricTensor, metrictensor
+
 ## conversions
 
 @pure choicevec(M,G,T) = T ∈ (Any,BigFloat,BigInt,Complex{BigFloat},Rational{BigInt},Complex{BigInt}) ? svec(M,G,T) : mvec(M,G,T)
@@ -288,7 +292,6 @@ end
 
 # Dyadic
 
-export TensorNested
 abstract type TensorNested{V,T} <: Manifold{V,T} end
 @pure Manifold(::T) where T<:TensorNested{V} where V = V
 @pure Manifold(::Type{T}) where T<:TensorNested{V} where V = V
@@ -301,6 +304,14 @@ transpose_row(t::Chain{V,1,<:Chain},i) where V = transpose_row(value(t),i,V)
 Base.transpose(t::Chain{V,1,<:Chain{V,1}}) where V = _transpose(value(t))
 Base.transpose(t::Chain{V,1,<:Chain{W,1}}) where {V,W} = _transpose(value(t),V)
 Base.inv(t::TensorNested,g) = inv(t)
+@generated function LinearAlgebra.tr(m::Chain{V,G,<:Chain{V,G},N}) where {V,G,N}
+    :(sum(Values($([:(m[$i][$i]) for i ∈ list(1,N)]...))))
+end
+for typ ∈ (:Spinor,:AntiSpinor,:Multivector)
+    @eval @generated function LinearAlgebra.tr(m::$typ{V,<:$typ{V},N}) where {V,N}
+        :(sum(Values($([:(m[$i][$i]) for i ∈ list(1,N)]...))))
+    end
+end
 
 Base.Matrix(t::TensorAlgebra) = matrix(t)
 
@@ -350,8 +361,6 @@ for (pinor,bas) ∈ ((:Spinor,:evenbasis),(:AntiSpinor,:oddbasis),(:Multivector,
     @eval display_matrix(m::$pinor{V,<:TensorAlgebra{W}}) where {V,W} = vcat(transpose([Submanifold(V),$bas(V)...]),hcat($bas(W),matrix(m)))
 end
 
-export Projector, Dyadic, Proj
-
 struct Projector{V,T,Λ} <: TensorNested{V,T}
     v::T
     λ::Λ
@@ -404,8 +413,6 @@ Chain(P::Dyadic{V}) where V = Chain{V}(P)
 
 # DiagonalOperator
 
-export DiagonalOperator
-
 struct DiagonalOperator{V,T<:TensorAlgebra{V}} <: TensorNested{V,T}
     v::T
     DiagonalOperator{V}(t::T) where {V,T<:TensorAlgebra{V}} = new{V,T}(t)
@@ -419,6 +426,7 @@ matrix(m::DiagonalOperator) = matrix(TensorOperator(m))
 getindex(t::DiagonalOperator,i::Int,j::Int) = i≠j ? zero(valuetype(value(t))) : value(value(t))[i]
 getindex(t::DiagonalOperator,i::Int) = value(t)(i)
 
+LinearAlgebra.tr(m::DiagonalOperator) = sum(value(value(m)))
 compound(m::DiagonalOperator{V,<:Chain{V,1}},::Val{0}) where V = DiagonalOperator(Chain{V,0}(1))
 @generated function compound(m::DiagonalOperator{V,<:Chain{V,1}},::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)]...)))
@@ -447,8 +455,6 @@ function show(io::IO, ::MIME"text/plain", t::DiagonalOperator)
     show_matrix(io, t, X)
 end
 
-export TensorOperator, Endomorphism
-
 struct TensorOperator{V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} <: TensorNested{V,T}
     v::T
     TensorOperator{V,W}(t::T) where {V,W,T<:TensorAlgebra{V,<:TensorAlgebra{W}}} = new{V,W,T}(t)
@@ -465,6 +471,7 @@ compound(m::TensorOperator,g) = TensorOperator(compound(value(m),g))
 compound(m::TensorOperator,g::Integer) = TensorOperator(compound(value(m),g))
 getindex(t::TensorOperator,i::Int,j::Int) = value(value(t.v)[j])[i]
 getindex(t::TensorOperator,i::Int) = value(t.v)[i]
+LinearAlgebra.tr(m::Endomorphism) = tr(value(m))
 
 for op ∈ (:(Base.inv),)
     @eval $op(t::Endomorphism{V,<:Chain}) where V = TensorOperator($op(value(t)))
@@ -529,8 +536,6 @@ end
 
 # Outermorphism
 
-export Outermorphism, outermorphism
-
 struct Outermorphism{V,T<:Tuple} <: TensorNested{V,T}
     v::T
     Outermorphism{V}(t::T) where {V,T<:Tuple} = new{V,T}(t)
@@ -547,6 +552,7 @@ outermorphism(t::Endomorphism{V,<:Simplex}) where V = outermorphism(value(t))
 value(t::Outermorphism) = t.v
 matrix(m::Outermorphism) = matrix(TensorOperator(m))
 getindex(t::Outermorphism{V},i::Int) where V = iszero(i) ? Chain{V,0}((Chain(One(V)),)) : t.v[i]
+LinearAlgebra.tr(m::Outermorphism) = 1+sum(tr.(value(m)))
 
 TensorOperator(t::Outermorphism{V}) where V = TensorOperator(Multivector{V}(vcat(Multivector(One(V)),value.(map.(Multivector,value.(t.v)))...)))
 
@@ -598,8 +604,6 @@ cayley(a::AbstractVector,b::AbstractVector,op) = TensorAlgebra{Manifold(Manifold
 
 # dyadic products
 
-export outer
-
 outer(a::Leibniz.Derivation,b::Chain{V,1}) where V= outer(V(a),b)
 outer(a::Chain{W},b::Leibniz.Derivation{T,1}) where {W,T} = outer(a,W(b))
 outer(a::Chain{W},b::Chain{V,1}) where {W,V} = Chain{V,1}(a.*value(b))
@@ -828,8 +832,6 @@ Base.:-(g::Chain{V,1,<:Chain{V,1}},t::LinearAlgebra.UniformScaling) where V = Ch
 
 # representation
 
-export operator, gradedoperator, evenoperator, oddoperator
-
 ⊘(a::TensorOperator{V,W,<:Chain{V,G}},b::TensorAlgebra{W}) where {V,W,G} = TensorOperator(Chain{V,G}(value(value(a)) .⊘ Ref(b)))
 for t ∈ (:Spinor,:AntiSpinor,:Multivector)
     @eval begin
@@ -896,8 +898,8 @@ end
 
 applyf(f,mat::TensorOperator) = f.(value(value(mat)))
 
-@pure metricfull(V) = Outermorphism(metrictensor(V))
-const metriceven,metricodd = metricfull,metricfull
+@pure metricextensor(V::TensorAlgebra) = Outermorphism(metrictensor(V))
+const metriceven,metricodd = metricextensor,metricextensor
 #metricfull(V) = TensorOperator(Multivector{V}(vcat(value.(map.(Multivector,value.(metrictensor.(V,list(0,mdims(V))))))...)))
 #metriceven(V) = TensorOperator(Spinor{V}(vcat(applyf.(Spinor,metrictensor.(V,evens(0,mdims(V))))...)))
 #metricodd(V) = TensorOperator(AntiSpinor{V}(vcat(applyf.(AntiSpinor,metrictensor.(V,evens(1,mdims(V))))...)))
@@ -906,7 +908,6 @@ struct MetricTensor{n,ℙ,g,Vars,Diff,Name} <: TensorBundle{n,ℙ,g,Vars,Diff,Na
     @pure MetricTensor{N,M,S,F,D,L}() where {N,M,S,F,D,L} = new{N,M,S,F,D,L}()
 end
 
-export MetricTensor, metrictensor
 @pure MetricTensor{N,M,S,F,D}() where {N,M,S,F,D} = MetricTensor{N,M,S,F,D,1}()
 @pure MetricTensor{N,M,S}() where {N,M,S} = MetricTensor{N,M,S,0,0}()
 @pure MetricTensor{N,M}(b::Values{N,<:Tuple}) where {N,M} = MetricTensor{N,M,metricsig(M,Values.(b))}()
@@ -971,18 +972,15 @@ end
 (M::MetricTensor)(b::T) where T<:AbstractVector{Int} = Submanifold{M}(b)
 (M::MetricTensor)(b::T) where T<:AbstractRange{Int} = Submanifold{M}(b)
 
-import LinearAlgebra: isdiag; export isdiag
 isdiag(::MetricTensor) = false
 
 # InducedMetric
 
-export InducedMetric
-
 struct InducedMetric end
 #=struct InducedMetric{V} <: TensorNested{V,Multivector{V}} end
 metrictensor(::InducedMetric{V}) where V = metrictensor(V)
-metricfull(::InducedMetric{V}) where V = metricfull(V)
-Base.show(io::IO,x::InducedMetric) = show(io,metricfull(x))=#
+metricextensor(::InducedMetric{V}) where V = metricextensor(V)
+Base.show(io::IO,x::InducedMetric) = show(io,metricextensor(x))=#
 
 isinduced(x) = false
 isinduced(::InducedMetric) = true
diff --git a/src/multivectors.jl b/src/multivectors.jl
index 59826f9..c0c6ef0 100644
--- a/src/multivectors.jl
+++ b/src/multivectors.jl
@@ -14,14 +14,18 @@
 
 export TensorTerm, TensorGraded, TensorMixed, Scalar, GradedVector, Bivector, Trivector
 export Submanifold, Single, Multivector, Spinor, SparseChain, MultiGrade, ChainBundle
-export Zero, One, Quaternion, GaussianInteger, AbstractSpinor
+export Zero, One, Chain, Phasor, Quaternion, GaussianInteger, AbstractSpinor, AntiSpinor
 export AbstractReal, AbstractComplex, AbstractRational, ScalarFloat, ScalarIrrational
-export AbstractInteger, AbstractBool, AbstractSigned, AbstractUnsigned, AntiSpinor
+export AbstractInteger, AbstractBool, AbstractSigned, AbstractUnsigned, CoSpinor, Simplex
 
 import AbstractTensors: Scalar, GradedVector, Bivector, Trivector
 import AbstractTensors: TensorTerm, TensorGraded, TensorMixed, equal
 import Leibniz: grade, antigrade, showvalue, basis, order
 
+import LinearAlgebra
+import LinearAlgebra: I, UniformScaling, isdiag, det, tr, dot, ⋅, cross, ×, rank, norm
+export UniformScaling, I, isdiag, det, tr, ⋅, cross, ×, contraction, points
+
 # symbolic print types
 
 import Leibniz: Fields, parval, mixed, mvecs, svecs, spinsum, spinsum_set
@@ -53,12 +57,6 @@ function showterm(io::IO,V,B::UInt,i::T,compact=get(io,:compact,false)) where T
     end
 end
 
-## pseudoscalar
-
-import LinearAlgebra
-import LinearAlgebra: I, UniformScaling
-export UniformScaling, I, points
-
 ## Chain{V,G,𝕂}
 
 @computed struct Chain{V,G,T} <: TensorGraded{V,G,T}
@@ -87,7 +85,6 @@ Chain(v::Chain{V,G,𝕂}) where {V,G,𝕂} = v
 #Simplex{V,W,T<:GradedVector{W},N} = Chain{V,1,T,N}
 Simplex{V,T<:GradedVector,N} = Chain{V,1,T,N}
 
-export Chain, Simplex
 getindex(m::Chain,i::Int) = m.v[i]
 getindex(m::Chain,i::UnitRange{Int}) = m.v[i]
 getindex(m::Chain,i::T) where T<:AbstractVector = m.v[i]
@@ -448,7 +445,7 @@ abstract type AbstractSpinor{V,T} <: TensorMixed{V,T} end
 
 @pure log2sub2(N) = log2sub(2N)
 
-for pinor ∈ (:Spinor,:AntiSpinor)
+for pinor ∈ (:Spinor,:CoSpinor)
     @eval begin
         @computed struct $pinor{V,T} <: AbstractSpinor{V,T}
             v::Values{1<<(mdims(V)-1),T}
@@ -484,6 +481,7 @@ for pinor ∈ (:Spinor,:AntiSpinor)
         equal(a::T,b::$pinor{V,S} where S) where T<:TensorTerm{V} where V = b==a
     end
 end
+const AntiSpinor = CoSpinor
 
 """
     Spinor{V,T} <: AbstractSpinor{V,T} <: TensorAlgebra{V,T}
@@ -504,20 +502,20 @@ Spinor{V,T}(v::Submanifold{V,G}) where {V,G,T} = Spinor{V,T}(one(T),v)
 end
 
 """
-    AntiSpinor{V,T} <: AbstractSpinor{V,T} <: TensorAlgebra{V,T}
+    CoSpinor{V,T} <: AbstractSpinor{V,T} <: TensorAlgebra{V,T}
 
 PsuedoSpinor (`odd` grade) type with pseudoscalar `V::Manifold` and scalar `T::Type`.
 """
-AntiSpinor{V}(val::Submanifold{V}) where V = AntiSpinor{V,Int}(1,val)
-AntiSpinor{V,T}(v::Submanifold{V,G}) where {V,G,T} = AntiSpinor{V,T}(one(T),v)
-@generated function AntiSpinor{V,𝕂}(val,v::Submanifold{V,G}) where {V,G,𝕂}
-    iseven(G) && error("$v is not expressible as an AntiSpinor")
+CoSpinor{V}(val::Submanifold{V}) where V = CoSpinor{V,Int}(1,val)
+CoSpinor{V,T}(v::Submanifold{V,G}) where {V,G,T} = CoSpinor{V,T}(one(T),v)
+@generated function CoSpinor{V,𝕂}(val,v::Submanifold{V,G}) where {V,G,𝕂}
+    iseven(G) && error("$v is not expressible as an CoSpinor")
     N = mdims(V)
     b = antiindex(N,UInt(basis(v)))
     if N<cache_limit
-        :(AntiSpinor{V}(Values($([i==b ? :val : zero(𝕂) for i ∈ 1:1<<(N-1)]...))))
+        :(CoSpinor{V}(Values($([i==b ? :val : zero(𝕂) for i ∈ 1:1<<(N-1)]...))))
     else
-        :(AntiSpinor{V,𝕂}(setanti!(zeros(mvecs($N,𝕂)),val,UInt(v),$(Val(N)))))
+        :(CoSpinor{V,𝕂}(setanti!(zeros(mvecs($N,𝕂)),val,UInt(v),$(Val(N)))))
     end
 end
 
@@ -527,10 +525,10 @@ for var ∈ ((:V,:T),(:T,),())
         N = mdims(V)
         chain_src(N,G,T,evens(0,N),:Spinor)
     end
-    @eval @generated function AntiSpinor{$(var...)}(t::Chain{V,G,T}) where {V,G,T}
-        iseven(G) && error("$t is not expressible as a AntiSpinor")
+    @eval @generated function CoSpinor{$(var...)}(t::Chain{V,G,T}) where {V,G,T}
+        iseven(G) && error("$t is not expressible as a CoSpinor")
         N = mdims(V)
-        chain_src(N,G,T,evens(1,N),:AntiSpinor)
+        chain_src(N,G,T,evens(1,N),:CoSpinor)
     end
 end
 
@@ -540,7 +538,7 @@ end
         #:(isodd(G) && return Zero(V)),
         Expr(:if,:(G==0),grade_src_chain(N,0,0),grade_src_chain_next(N,N-1,spinsum,isodd,T)))
 end
-@generated function (t::AntiSpinor{V,T})(G::Int) where {V,T}
+@generated function (t::CoSpinor{V,T})(G::Int) where {V,T}
     N = mdims(V)
     Expr(:block,:(0 <= G <= $N || throw(BoundsError(t, G))),
         #:(iseven(G) && return Zero(V)),
@@ -551,7 +549,7 @@ end
     Expr(:block,:(0 <= G <= $N || throw(BoundsError(t, G))),
         Expr(:if,:(G==0),grade_src(N,0,0),grade_src_next(N,N-1,spinsum,isodd,T)))
 end
-@generated function getindex(t::AntiSpinor{V,T},G::Int) where {V,T}
+@generated function getindex(t::CoSpinor{V,T},G::Int) where {V,T}
     N = mdims(V)
     Expr(:block,:(0 <= G <= $N || throw(BoundsError(t, G))),
         Expr(:if,:(G==0),grade_src(N,0,0,iseven),grade_src_next(N,N-1,antisum,iseven,T)))
@@ -562,7 +560,7 @@ end
     isodd(G) && return zeros(svec(N,G,T))
     return grade_src(N,G,spinsum(N,G))
 end
-@generated function getindex(t::AntiSpinor{V,T},::Val{G}) where {V,T,G}
+@generated function getindex(t::CoSpinor{V,T},::Val{G}) where {V,T,G}
     N = mdims(V)
     0 <= G <= N || throw(BoundsError(t, G))
     iseven(G) && return zeros(svec(N,G,T))
@@ -570,7 +568,7 @@ end
 end
 
 (m::Spinor{V,T})(g::Val{G}) where {V,T,G} = isodd(G) ? Zero(V) : Chain{V,G,T}(m[g])
-(m::AntiSpinor{V,T})(g::Val{G}) where {V,T,G} = iseven(G) ? Zero(V) : Chain{V,G,T}(m[g])
+(m::CoSpinor{V,T})(g::Val{G}) where {V,T,G} = iseven(G) ? Zero(V) : Chain{V,G,T}(m[g])
 function (m::Spinor{V,T})(g::Val{G},i::Int) where {V,T,G}
     if isodd(G)
         return Zero(V)
@@ -578,7 +576,7 @@ function (m::Spinor{V,T})(g::Val{G},i::Int) where {V,T,G}
         Single{V,G,DirectSum.getbasis(V,indexbasis(mdims(V),G)[i]),T}(m[g][i])
     end
 end
-function (m::AntiSpinor{V,T})(g::Val{G},i::Int) where {V,T,G}
+function (m::CoSpinor{V,T})(g::Val{G},i::Int) where {V,T,G}
     if iseven(G)
         return Zero(V)
     else
@@ -591,7 +589,7 @@ end
     bs = spinsum_set(N)
     :(Multivector{V,T}($(Expr(:call,:Values,vcat([iseven(G) ? [:(@inbounds t.v[$(i+bs[G+1])]) for i ∈ list(1,binomial(N,G))] : zeros(T,binomial(N,G)) for G ∈ list(0,N)]...)...))))
 end
-@generated function Multivector{V}(t::AntiSpinor{V,T}) where {V,T}
+@generated function Multivector{V}(t::CoSpinor{V,T}) where {V,T}
     N = mdims(V)
     bs = antisum_set(N)
     :(Multivector{V,T}($(Expr(:call,:Values,vcat([isodd(G) ? [:(@inbounds t.v[$(i+bs[G+1])]) for i ∈ list(1,binomial(N,G))] : zeros(T,binomial(N,G)) for G ∈ list(0,N)]...)...))))
@@ -605,7 +603,7 @@ end
         iseven(grade(B)) ? a.v[bladeindex(mdims(V),UInt(B))]*B : zero(T)*B
     end
 end
-@pure function Base.getproperty(a::AntiSpinor{V,T},v::Symbol) where {V,T}
+@pure function Base.getproperty(a::CoSpinor{V,T},v::Symbol) where {V,T}
     return if v == :v
         getfield(a,:v)
     else
@@ -626,7 +624,7 @@ function Base.show(io::IO, m::Spinor{V,T}) where {V,T}
         end
     end
 end
-function Base.show(io::IO, m::AntiSpinor{V,T}) where {V,T}
+function Base.show(io::IO, m::CoSpinor{V,T}) where {V,T}
     N,compact = mdims(V),get(io,:compact,false)
     io = compactio(io)
     bs = antisum_set(N)
@@ -655,13 +653,13 @@ function equal(a::Spinor{V,S} where S,b::T) where T<:TensorTerm{V,G} where {V,G}
     i = spinindex(mdims(V),UInt(basis(b)))
     @inbounds a.v[i] == value(b) && prod(a.v[list(1,i-1)] .== 0) && prod(a.v[list(i+1,1<<(mdims(V)-1))] .== 0)
 end
-function equal(a::AntiSpinor{V,T},b::Chain{V,G,S}) where {V,T,G,S}
+function equal(a::CoSpinor{V,T},b::Chain{V,G,S}) where {V,T,G,S}
     iseven(G) && (return iszero(b) && iszero(a))
     N = mdims(V)
     r,R = antisum(N,G), N≠G ? antisum(N,G+1) : 1<<(N-1)+1
     @inbounds prod(a[Val(G)] .== b.v) && prod(a.v[list(1,r)] .== 0) && prod(a.v[list(R+1,1<<(N-1))] .== 0)
 end
-function equal(a::AntiSpinor{V,S} where S,b::T) where T<:TensorTerm{V,G} where {V,G}
+function equal(a::CoSpinor{V,S} where S,b::T) where T<:TensorTerm{V,G} where {V,G}
     i = antiindex(mdims(V),UInt(basis(b)))
     @inbounds a.v[i] == value(b) && prod(a.v[list(1,i-1)] .== 0) && prod(a.v[list(i+1,1<<(mdims(V)-1))] .== 0)
 end
@@ -669,8 +667,8 @@ for T ∈ Fields
     @eval begin
         ==(a::T,b::Spinor{V,S,G} where {V,S}) where {T<:$T,G} = (v=value(b);@inbounds (a==v[1])*prod(0 .== v[list(2,1<<(mdims(V)-1))]))
         ==(a::Spinor{V,S,G} where {V,S},b::T) where {T<:$T,G} = b == a
-        ==(a::T,b::AntiSpinor{V,S,G} where {V,S}) where {T<:$T,G} = iszero(b)
-        ==(a::AntiSpinor{V,S,G} where {V,S},b::T) where {T<:$T,G} = iszero(a)
+        ==(a::T,b::CoSpinor{V,S,G} where {V,S}) where {T<:$T,G} = iszero(b)
+        ==(a::CoSpinor{V,S,G} where {V,S},b::T) where {T<:$T,G} = iszero(a)
     end
 end
 
@@ -731,9 +729,9 @@ Multivector{V,T}(z::PseudoCouple{V,B,T}) where {V,B,T} = Multivector{V}(imaginar
 Spinor{V,𝕂}(z::Couple{V,B,𝕂}) where {V,B,𝕂} = Spinor{V}(scalar(z), imaginary(z))
 Spinor{V,𝕂}(z::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = Spinor{V}(imaginary(z), volume(z))
 
-@generated AntiSpinor{V}(a::Single{V,L},b::Single{V,G}) where {V,L,G} = adderanti(a,b,:+)
-AntiSpinor{V}(val::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = AntiSpinor{V,𝕂}(val)
-AntiSpinor{V,𝕂}(z::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = AntiSpinor{V}(imaginary(z),volume(z))
+@generated CoSpinor{V}(a::Single{V,L},b::Single{V,G}) where {V,L,G} = adderanti(a,b,:+)
+CoSpinor{V}(val::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = CoSpinor{V,𝕂}(val)
+CoSpinor{V,𝕂}(z::PseudoCouple{V,B,𝕂}) where {V,B,𝕂} = CoSpinor{V}(imaginary(z),volume(z))
 
 (t::Couple{V,B})(G::Int) where {V,B} = grade(B) == G ? imaginary(t) : iszero(G) ? scalar(t) : Zero(V)
 (t::PseudoCouple{V,B})(G::Int) where {V,B} = grade(B) == G ? imaginary(t) : G==mdims(V) ? volume(t) : Zero(V)
@@ -828,8 +826,8 @@ for (eq,qe) ∈ ((:(Base.:(==)),:equal), (:(Base.isapprox),:(Base.isapprox)))
             $qe(a::Multivector{V},b::$couple{V}) where V = $eq(a,multispin(b))
             $qe(a::$couple{V,B},b::Spinor{V}) where {V,B} = $eq(multispin(a),b)
             $qe(a::Spinor{V},b::$couple{V,B}) where {V,B} = $eq(a,multispin(b))
-            $qe(a::$couple{V,B},b::AntiSpinor{V}) where {V,B} = $eq(multispin(a),b)
-            $qe(a::AntiSpinor{V},b::$couple{V,B}) where {V,B} = $eq(a,multispin(b))
+            $qe(a::$couple{V,B},b::CoSpinor{V}) where {V,B} = $eq(multispin(a),b)
+            $qe(a::CoSpinor{V},b::$couple{V,B}) where {V,B} = $eq(a,multispin(b))
         end
     end
 end
@@ -860,8 +858,6 @@ end
 
 ## Phasor{V,B}
 
-export Phasor, ∠, radius
-
 """
     Phasor{V,B,T} <: AbstractSpinor{V,T} <: TensorAlgebra{V,T}
 
@@ -952,15 +948,14 @@ import Base: isinf, isapprox
 import AbstractTensors: antiabs, antiabs2, geomabs, unit, unitize, unitnorm
 import AbstractTensors: value, valuetype, scalar, isscalar, involute, even, odd
 import AbstractTensors: vector, isvector, bivector, isbivector, volume, isvolume, ⋆
-import LinearAlgebra: rank, norm
-export gdims, betti, χ, unit
+export gdims, betti, χ, unit, ∠, radius
 export basis, grade, pseudograde, antigrade, hasinf, hasorigin, scalar, norm, unitnorm
 export valuetype, scalar, isscalar, vector, isvector, indices, imaginary, unitize, geomabs
 export bivector, isbivector, trivector, istrivector, volume, isvolume, antiabs, antiabs2
 
 const Imaginary{V,T} = Spinor{V,T,2}
 const Quaternion{V,T} = Spinor{V,T,4}
-const AntiQuaternion{V,T} = AntiSpinor{V,T,4}
+const AntiQuaternion{V,T} = CoSpinor{V,T,4}
 const LipschitzInteger{V,T<:Integer} = Quaternion{V,T}
 const GaussianInteger{V,B,T<:Integer} = Couple{V,B,T}
 #const PointCloud{T<:Chain{V,1} where V} = AbstractVector{T}
@@ -983,13 +978,13 @@ const ScalarIrrational = Union{AbstractIrrational,Single{V,G,B,<:AbstractIrratio
 Couple(m::Imaginary{V}) where V = Couple{V,Submanifold(V)}(Complex(m))
 
 Spinor{V}(t::Spinor{V}) where V = t
-AntiSpinor{V}(t::AntiSpinor{V}) where V = t
+CoSpinor{V}(t::CoSpinor{V}) where V = t
 Multivector{V}(t::Multivector{V}) where V = t
 
 multispin(t::Multivector) = t
 multispin(t::Spinor) = t
-multispin(t::AntiSpinor) = t
-multispin(t::TensorGraded) = iseven(grade(t)) ? Spinor(t) : AntiSpinor(t)
+multispin(t::CoSpinor) = t
+multispin(t::TensorGraded) = iseven(grade(t)) ? Spinor(t) : CoSpinor(t)
 function multispin(t::Couple{V,B}) where {V,B}
     iseven(grade(B)) ? Spinor(t) : Multivector(t)
 end
@@ -997,7 +992,7 @@ function multispin(t::PseudoCouple{V,B}) where {V,B}
     if iseven(grade(V)) && iseven(grade(B))
         Spinor(t)
     elseif isodd(grade(V)) && isodd(grade(B))
-        AntiSpinor(t)
+        CoSpinor(t)
     else
         Multivector(t)
     end
@@ -1019,7 +1014,7 @@ const quatvalues = quatvalue
 @inline value(m::Chain,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
 @inline value(m::Multivector,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
 @inline value(m::Spinor,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
-@inline value(m::AntiSpinor,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
+@inline value(m::CoSpinor,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(T,m.v) : m.v
 @inline value(m::Couple,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(Complex{T},Complex(m)) : Complex(m)
 @inline value(m::PseudoCouple,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(Complex{T},Complex(m)) : Complex(m)
 #@inline value(m::Phasor,T=valuetype(m)) = T∉(valuetype(m),Any) ? convert(Complex{T},m.v) : m.v
@@ -1028,7 +1023,7 @@ const quatvalues = quatvalue
 
 Base.isapprox(a::S,b::T) where {S<:Multivector,T<:Multivector} = Manifold(a)==Manifold(b) && DirectSum.:≈(value(a),value(b))
 Base.isapprox(a::S,b::T) where {S<:Spinor,T<:Spinor} = Manifold(a)==Manifold(b) && DirectSum.:≈(value(a),value(b))
-Base.isapprox(a::S,b::T) where {S<:AntiSpinor,T<:AntiSpinor} = Manifold(a)==Manifold(b) && DirectSum.:≈(value(a),value(b))
+Base.isapprox(a::S,b::T) where {S<:CoSpinor,T<:CoSpinor} = Manifold(a)==Manifold(b) && DirectSum.:≈(value(a),value(b))
 
 @inline scalar(z::Couple{V}) where V = Single{V}(realvalue(z))
 @inline scalar(z::PseudoCouple{V,B}) where {V,B} = grade(B)==0 ? Single{V}(realvalue(z)) : Zero(V)
@@ -1036,29 +1031,29 @@ Base.isapprox(a::S,b::T) where {S<:AntiSpinor,T<:AntiSpinor} = Manifold(a)==Mani
 @inline scalar(t::Chain{V,0,T}) where {V,T} = @inbounds Single{V}(t.v[1])
 @inline scalar(t::Multivector{V}) where V = @inbounds Single{V}(t.v[1])
 @inline scalar(t::Spinor{V}) where V = @inbounds Single{V}(t.v[1])
-@inline scalar(t::AntiSpinor{V}) where V = Zero(V)
+@inline scalar(t::CoSpinor{V}) where V = Zero(V)
 @inline vector(z::Couple{V,B}) where {V,B} = grade(B)==1 ? imaginary(z) : Zero(V)
 @inline vector(z::PseudoCouple{V,B}) where {V,B} = grade(B)==1 ? imaginary(z) : grade(V)==1 ? volume(z) : Zero(V)
 @inline vector(t::Multivector) = t(Val(1))
 @inline vector(t::Spinor{V}) where V = Zero(V)
-@inline vector(t::AntiSpinor) = t(Val(1))
+@inline vector(t::CoSpinor) = t(Val(1))
 @inline bivector(z::Couple{V,B}) where {V,B} = grade(B)==2 ? imaginary(z) : Zero(V)
 @inline bivector(z::PseudoCouple{V,B}) where {V,B} = grade(B)==2 ? imaginary(z) : grade(V)==2 ? volume(z) : Zero(V)
 @inline bivector(t::Multivector) = t(Val(2))
 @inline bivector(t::Spinor) = t(Val(2))
-@inline bivector(t::AntiSpinor{V}) where V = Zero(V)
+@inline bivector(t::CoSpinor{V}) where V = Zero(V)
 @inline trivector(z::Couple{V,B}) where {V,B} = grade(B)==3 ? imaginarya(z) : Zero(V)
 @inline trivector(z::PseudoCouple{V,B}) where {V,B} = grade(B)==3 ? imaginary(z) : grade(V)==3 ? volume(z) : Zero(V)
 @inline trivector(t::Multivector) = t(Val(3))
 @inline trivector(t::Spinor{V}) where V = Zero(V)
-@inline trivector(t::AntiSpinor) = t(Val(3))
+@inline trivector(t::CoSpinor) = t(Val(3))
 #@inline bivector(t::Quaternion{V}) where V = @inbounds Chain{V,2}(t.v[2],t.v[3],t.v[4])
 @inline volume(t::Chain{V,G,T,1}) where {V,G,T} = @inbounds Single{V,G,basis(V)}(t.v[1])
 @inline volume(z::Couple{V,B}) where {V,B} = grade(B)==grade(V) ? Single{V,grade(B),B}(imagvalue(z)) : Zero(V)
 @inline volume(z::PseudoCouple{V}) where V = Single{V,mdims(V),Submanifold(V)}(imagvalue(z))
 @inline volume(t::Multivector{V}) where V = @inbounds Single{V,mdims(V),Submanifold(V)}(t.v[end])
 @inline volume(t::Spinor{V}) where V = iseven(grade(V)) ? (@inbounds Single{V,mdims(V),Submanifold(V)}(t.v[end])) : Zero(V)
-@inline volume(t::AntiSpinor{V}) where V = isodd(grade(V)) ? (@inbounds Single{V,mdims(V),Submanifold(V)}(t.v[end])) : Zero(V)
+@inline volume(t::CoSpinor{V}) where V = isodd(grade(V)) ? (@inbounds Single{V,mdims(V),Submanifold(V)}(t.v[end])) : Zero(V)
 @inline imaginary(z::Couple{V,B}) where {V,B} = Single{V,grade(B),B}(imagvalue(z))
 @inline imaginary(z::PseudoCouple{V,B}) where {V,B} = Single{V,grade(B),B}(realvalue(z))
 @inline imaginary(z::Quaternion) = bivector(z)
@@ -1081,43 +1076,43 @@ end
 @pure maxgrade(t::Couple{V,B}) where {V,B} = grade(B)
 @pure maxgrade(t::PseudoCouple{V}) where V = grade(V)
 @pure maxgrade(t::Spinor{V}) where V = isodd(mdims(V)) ? mdims(V)-1 : mdims(V)
-@pure maxgrade(t::AntiSpinor{V}) where V = isodd(mdims(V)) ? mdims(V) : mdims(V)-1
+@pure maxgrade(t::CoSpinor{V}) where V = isodd(mdims(V)) ? mdims(V) : mdims(V)-1
 @pure maxgrade(t::Multivector{V}) where V = mdims(V)
 @pure mingrade(t::TensorGraded) = grade(t)
 @pure mingrade(t::Couple) = 0
 @pure mingrade(t::PseudoCouple{V,B}) where {V,B} = grade(B)
 @pure mingrade(t::Spinor) = 0
-@pure mingrade(t::AntiSpinor) = 1
+@pure mingrade(t::CoSpinor) = 1
 @pure mingrade(t::Multivector) = 0
 
 @pure maxgrade(t::Type{<:TensorGraded}) = grade(t)
 @pure maxgrade(t::Type{<:Couple{V,B}}) where {V,B} = grade(B)
 @pure maxgrade(t::Type{<:PseudoCouple{V}}) where V = grade(V)
 @pure maxgrade(t::Type{<:Spinor{V}}) where V = isodd(mdims(V)) ? mdims(V)-1 : mdims(V)
-@pure maxgrade(t::Type{<:AntiSpinor{V}}) where V = isodd(mdims(V)) ? mdims(V) : mdims(V)-1
+@pure maxgrade(t::Type{<:CoSpinor{V}}) where V = isodd(mdims(V)) ? mdims(V) : mdims(V)-1
 @pure maxgrade(t::Type{<:Multivector{V}}) where V = mdims(V)
 @pure mingrade(t::Type{<:TensorGraded}) = grade(t)
 @pure mingrade(t::Type{<:Couple}) = 0
 @pure mingrade(t::Type{<:PseudoCouple{V,B}}) where {V,B} = grade(B)
 @pure mingrade(t::Type{<:Spinor}) = 0
-@pure mingrade(t::Type{<:AntiSpinor}) = 1
+@pure mingrade(t::Type{<:CoSpinor}) = 1
 @pure mingrade(t::Type{<:Multivector}) = 0
 
 @pure nextgrade(t::Spinor) = 2
-@pure nextgrade(t::AntiSpinor) = 2
+@pure nextgrade(t::CoSpinor) = 2
 @pure nextgrade(t::Multivector) = 1
 @pure nextgrade(t::Type{<:Spinor}) = 2
-@pure nextgrade(t::Type{<:AntiSpinor}) = 2
+@pure nextgrade(t::Type{<:CoSpinor}) = 2
 @pure nextgrade(t::Type{<:Multivector}) = 1
 @pure nextmingrade(t) = mingrade(t)+nextgrade(t)
 @pure nextmaxgrade(t) = maxgrade(t)-nextgrade(t)
 
 @pure maxpseudograde(t::Multivector) = maxgrade(t)
 @pure maxpseudograde(t::Spinor{V}) where V = mdims(V)
-@pure maxpseudograde(t::AntiSpinor{V}) where V = mdims(V)-1
+@pure maxpseudograde(t::CoSpinor{V}) where V = mdims(V)-1
 @pure maxpseudograde(t::Type{<:Multivector}) = maxgrade(t)
 @pure maxpseudograde(t::Type{<:Spinor{V}}) where V = mdims(V)
-@pure maxpseudograde(t::Type{<:AntiSpinor{V}}) where V = mdims(V)-1
+@pure maxpseudograde(t::Type{<:CoSpinor{V}}) where V = mdims(V)-1
 @pure nextmaxpseudograde(t) = maxpseudograde(t)-nextgrade(t)
 
 Leibniz.count_gdims(t::Tuple{Vector{<:Chain},Vector{Int}}) = count_gdims(t[1][findall(x->!iszero(x),t[2])])
diff --git a/src/parity.jl b/src/parity.jl
index b1a023e..8559c02 100644
--- a/src/parity.jl
+++ b/src/parity.jl
@@ -24,8 +24,8 @@ export complementleftanti, complementrightanti
 
 ## reverse
 
-import Base: reverse, conj, ~
-export involute, clifford, pseudoreverse, antireverse
+import Base: reverse, conj, ~, signbit, imag, real
+export involute, clifford, pseudoreverse, antireverse, odd, even, angular, radial, ₊, ₋, ǂ
 
 ## product parities
 
@@ -420,9 +420,6 @@ for par ∈ (:conformal,:regressive,:interior)
     end
 end
 
-import Base: signbit, imag, real
-export odd, even, angular, radial, ₊, ₋, ǂ
-
 @pure signbit(V::T) where T<:Manifold = (ib=indexbasis(rank(V)); parity.(Ref(V),ib,ib))
 @pure signbit(V::T,G) where T<:Manifold = (ib=indexbasis(rank(V),G); parity.(Ref(V),ib,ib))
 @pure angular(V::T) where T<:Manifold = Values(findall(signbit(V))...)
@@ -448,9 +445,9 @@ Base.isodd(t::Zero) = true
 Base.iseven(t::TensorGraded{V,G}) where {V,G} = iseven(G) ? true : iszero(t)
 Base.isodd(t::TensorGraded{V,G}) where {V,G} = isodd(G) ? true : iszero(t)
 Base.iseven(t::Spinor) = true
-Base.iseven(t::AntiSpinor) = iszero(t)
+Base.iseven(t::CoSpinor) = iszero(t)
 Base.isodd(t::Spinor) = iszero(t)
-Base.isodd(t::AntiSpinor) = true
+Base.isodd(t::CoSpinor) = true
 Base.iseven(t::Couple{V,B}) where {V,B} = iseven(grade(B)) ? true : iszero(imaginary(t))
 Base.isodd(t::Couple{V,B}) where {V,B} = isodd(grade(B)) ? iszero(scalar(t)) : iszero(t)
 Base.iseven(t::PseudoCouple{V,B}) where {V,B} = iseven(imaginary(t)) && iseven(volume(t))
@@ -458,10 +455,10 @@ Base.isodd(t::PseudoCouple{V,B}) where {V,B} = isodd(imaginary(t)) && isodd(volu
 Base.iseven(t::Multivector) = norm(t) ≈ norm(even(t))
 Base.isodd(t::Multivector) = norm(t) ≈ norm(odd(t))
 
-even(t::AntiSpinor{V}) where V = Zero{V}()
+even(t::CoSpinor{V}) where V = Zero{V}()
 odd(t::Spinor{V}) where V = Zero{V}()
 even(t::Spinor) = t
-odd(t::AntiSpinor) = t
+odd(t::CoSpinor) = t
 even(t::Couple{V,B}) where {V,B} = iseven(grade(B)) ? t : scalar(t)
 odd(t::Couple{V,B}) where {V,B} = isodd(grade(B)) ? imaginary(t) : Zero{V}()
 even(t::PseudoCouple{V,B}) where {V,B} = even(imaginary(t)) + even(volume(t))
diff --git a/src/products.jl b/src/products.jl
index f1a9a1b..2bfdad2 100644
--- a/src/products.jl
+++ b/src/products.jl
@@ -490,13 +490,13 @@ plus(b::Multivector{V},a::Submanifold{V,G}) where {V,G} = plus(a,b)
 plus(b::Multivector{V},a::Single{V,G}) where {V,G} = plus(a,b)
 plus(b::Spinor{V},a::Submanifold{V,G}) where {V,G} = plus(a,b)
 plus(b::Spinor{V},a::Single{V,G}) where {V,G} = plus(a,b)
-plus(b::AntiSpinor{V},a::Submanifold{V,G}) where {V,G} = plus(a,b)
-plus(b::AntiSpinor{V},a::Single{V,G}) where {V,G} = plus(a,b)
+plus(b::CoSpinor{V},a::Submanifold{V,G}) where {V,G} = plus(a,b)
+plus(b::CoSpinor{V},a::Single{V,G}) where {V,G} = plus(a,b)
 -(t::Submanifold) = Single(-value(t),t)
 -(a::Chain{V,G}) where {V,G} = Chain{V,G}(-value(a))
 -(a::Multivector{V}) where V = Multivector{V}(-value(a))
 -(a::Spinor{V}) where V = Spinor{V}(-value(a))
--(a::AntiSpinor{V}) where V = AntiSpinor{V}(-value(a))
+-(a::CoSpinor{V}) where V = CoSpinor{V}(-value(a))
 -(a::Couple{V,B}) where {V,B} = Couple{V,B}(-a.v)
 -(a::PseudoCouple{V,B}) where {V,B} = PseudoCouple{V,B}(-a.v)
 ⟑(a::Single{V,0},b::Chain{V,G}) where {V,G} = Chain{V,G}(a.v*b.v)
@@ -537,8 +537,8 @@ for (op,po) ∈ ((:plus,:+),(:minus,:-))
         $op(a::Couple{V},b::PseudoCouple{V}) where V = $op($op(a,imaginary(b)),volume(b))
         $op(a::PseudoCouple{V},b::Couple{V}) where V = $op(imaginary(a),b)+volume(a)
         $op(a::Phasor{V},b::Phasor{V}) where V = $op(Couple(a),Couple(b))
-        $op(a::Spinor{V},b::AntiSpinor{V}) where V = $op(Multivector(a),Multivector(b))
-        $op(a::AntiSpinor{V},b::Spinor{V}) where V = $op(Multivector(a),Multivector(b))
+        $op(a::Spinor{V},b::CoSpinor{V}) where V = $op(Multivector(a),Multivector(b))
+        $op(a::CoSpinor{V},b::Spinor{V}) where V = $op(Multivector(a),Multivector(b))
     end
 end
 
@@ -683,8 +683,8 @@ for (couple,calar) ∈ ((:Couple,:scalar),(:PseudoCouple,:volume))
         $op(a::$couple{V},b::Multivector{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::Spinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
         $op(a::$couple{V},b::Spinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
-        $op(a::AntiSpinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
-        $op(a::$couple{V},b::AntiSpinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
+        $op(a::CoSpinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
+        $op(a::$couple{V},b::CoSpinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::Chain{V,G},b::$couple{V},$(args...)) where {V,G} = (G==0 || G==mdims(V)) ? $op(Single(a),b,$(args...)) : $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
         $op(a::$couple{V},b::Chain{V,G},$(args...)) where {V,G} = (G==0 || G==mdims(V)) ? $op(a,Single(b),$(args...)) : $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::TensorTerm{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
@@ -705,8 +705,8 @@ for (couple,calar) ∈ ((:Couple,:scalar),(:PseudoCouple,:volume))
         ∧(a::$couple{V},b::Multivector{V}) where V = ($calar(a)∧b) + (imaginary(a)∧b)
         ∧(a::Spinor{V},b::$couple{V}) where V = (a∧$calar(b)) + (a∧imaginary(b))
         ∧(a::$couple{V},b::Spinor{V}) where V = ($calar(a)∧b) + (imaginary(a)∧b)
-        ∧(a::AntiSpinor{V},b::$couple{V}) where V = (a∧$calar(b)) + (a∧imaginary(b))
-        ∧(a::$couple{V},b::AntiSpinor{V}) where V = ($calar(a)∧b) + (imaginary(a)∧b)
+        ∧(a::CoSpinor{V},b::$couple{V}) where V = (a∧$calar(b)) + (a∧imaginary(b))
+        ∧(a::$couple{V},b::CoSpinor{V}) where V = ($calar(a)∧b) + (imaginary(a)∧b)
         ∧(a::Chain{V},b::$couple{V}) where V = (a∧$calar(b)) + (a∧imaginary(b))
         ∧(a::$couple{V},b::Chain{V}) where V = ($calar(a)∧b) + (imaginary(a)∧b)
         ∧(a::TensorTerm{V,0},b::$couple{V}) where V = a⟑b
@@ -732,8 +732,8 @@ for (couple,calar) ∈ ((:Couple,:scalar),(:PseudoCouple,:volume))
         ∨(a::$couple{V},b::Multivector{V}) where V = ($calar(a)∨b) + (imaginary(a)∨b)
         ∨(a::Spinor{V},b::$couple{V}) where V = (a∨$calar(b)) + (a∨imaginary(b))
         ∨(a::$couple{V},b::Spinor{V}) where V = ($calar(a)∨b) + (imaginary(a)∨b)
-        ∨(a::AntiSpinor{V},b::$couple{V}) where V = (a∨$calar(b)) + (a∨imaginary(b))
-        ∨(a::$couple{V},b::AntiSpinor{V}) where V = ($calar(a)∨b) + (imaginary(a)∨b)
+        ∨(a::CoSpinor{V},b::$couple{V}) where V = (a∨$calar(b)) + (a∨imaginary(b))
+        ∨(a::$couple{V},b::CoSpinor{V}) where V = ($calar(a)∨b) + (imaginary(a)∨b)
         ∨(a::Chain{V},b::$couple{V}) where V = (a∨$calar(b)) + (a∨imaginary(b))
         ∨(a::$couple{V},b::Chain{V}) where V = ($calar(a)∨b) + (imaginary(a)∨b)
     end
@@ -766,8 +766,8 @@ for (couple,calar) ∈ ((:Couple,:scalar),(:PseudoCouple,:volume))
         $op(a::$couple{V},b::Multivector{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::Spinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
         $op(a::$couple{V},b::Spinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
-        $op(a::AntiSpinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
-        $op(a::$couple{V},b::AntiSpinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
+        $op(a::CoSpinor{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
+        $op(a::$couple{V},b::CoSpinor{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::Chain{V},b::$couple{V},$(args...)) where V = $op(a,$calar(b),$(args...)) + $op(a,imaginary(b),$(args...))
         $op(a::$couple{V},b::Chain{V},$(args...)) where V = $op($calar(a),b,$(args...)) + $op(imaginary(a),b,$(args...))
         $op(a::$couple{V},b::TensorTerm{V,0},$(args...)) where V = a⟑b
@@ -813,8 +813,8 @@ for F ∈ Fields
         *(a::Multivector{V},b::F) where {F<:$F,V} = Multivector{V}(a.v*b)
         *(a::F,b::Spinor{V}) where {F<:$F,V} = Spinor{V}(a*b.v)
         *(a::Spinor{V},b::F) where {F<:$F,V} = Spinor{V}(a.v*b)
-        *(a::F,b::AntiSpinor{V}) where {F<:$F,V} = AntiSpinor{V}(a*b.v)
-        *(a::AntiSpinor{V},b::F) where {F<:$F,V} = AntiSpinor{V}(a.v*b)
+        *(a::F,b::CoSpinor{V}) where {F<:$F,V} = CoSpinor{V}(a*b.v)
+        *(a::CoSpinor{V},b::F) where {F<:$F,V} = CoSpinor{V}(a.v*b)
         *(a::F,b::Chain{V,G}) where {F<:$F,V,G} = Chain{V,G}(a*b.v)
         *(a::Chain{V,G},b::F) where {F<:$F,V,G} = Chain{V,G}(a.v*b)
         *(a::F,b::Single{V,G,B,T} where B) where {F<:$F,V,G,T} = Single{V,G}($Sym.:∏(a,b.v),basis(b))
@@ -848,7 +848,7 @@ for (op,po) ∈ ((:+,:plus),(:-,:minus))
         @generated function $po(a::TensorTerm{V,G},b::Spinor{V,T}) where {V,G,T}
             adder(a,b,$(QuoteNode(op)))
         end
-        @generated function $po(a::TensorTerm{V,G},b::AntiSpinor{V,T}) where {V,G,T}
+        @generated function $po(a::TensorTerm{V,G},b::CoSpinor{V,T}) where {V,G,T}
             adder(a,b,$(QuoteNode(op)))
         end
     end
@@ -856,7 +856,7 @@ end
 @generated minus(b::Chain{V,G,T},a::TensorTerm{V,G}) where {V,G,T} = adder(a,b,:-,true)
 @generated minus(b::Chain{V,G,T},a::TensorTerm{V,L}) where {V,G,T,L} = adder(a,b,:-,true)
 @generated minus(b::Spinor{V,T},a::TensorTerm{V,G}) where {V,G,T} = adder(a,b,:-,true)
-@generated minus(b::AntiSpinor{V,T},a::TensorTerm{V,G}) where {V,G,T} = adder(a,b,:-,true)
+@generated minus(b::CoSpinor{V,T},a::TensorTerm{V,G}) where {V,G,T} = adder(a,b,:-,true)
 @generated minus(b::Multivector{V,T},a::TensorTerm{V,G}) where {V,G,T} = adder(a,b,:-,true)
 
 @eval begin
@@ -953,7 +953,7 @@ end
             Spinor{dual(V)}(out)
         end end
     end
-    @generated function Base.adjoint(m::AntiSpinor{V,T}) where {V,T}
+    @generated function Base.adjoint(m::CoSpinor{V,T}) where {V,T}
         CONJ,VEC = conjvec(m)
         TF = T ∉ FieldsBig ? :Any : :T
         if mdims(V)<cache_limit
@@ -966,9 +966,9 @@ end
                         @inbounds setanti!_pre(out,:($CONJ(@inbounds m.v[$(ps[g]+i)])),dual(V,ib[i],M))
                     end
                 end
-                return :(AntiSpinor{$(dual(V))}($(Expr(:call,tvecs(N,TF),out...))))
+                return :(CoSpinor{$(dual(V))}($(Expr(:call,tvecs(N,TF),out...))))
             else
-                return :(AntiSpinor{$(dual(V))}($CONJ.(value(m))))
+                return :(CoSpinor{$(dual(V))}($CONJ.(value(m))))
             end
         else return quote
             if isdyadic(V)
@@ -983,7 +983,7 @@ end
             else
                 out = $CONJ.(value(m))
             end
-            AntiSpinor{dual(V)}(out)
+            CoSpinor{dual(V)}(out)
         end end
     end
 end
@@ -1009,8 +1009,8 @@ function generate_products(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj
         *(a::Multivector{V},b::F) where {F<:$EF,V} = Multivector{V}(a.v*b)
         *(a::F,b::Spinor{V}) where {F<:$EF,V} = Spinor{V}(a*b.v)
         *(a::Spinor{V},b::F) where {F<:$EF,V} = Spinor{V}(a.v*b)
-        *(a::F,b::AntiSpinor{V}) where {F<:$EF,V} = AntiSpinor{V}(a*b.v)
-        *(a::AntiSpinor{V},b::F) where {F<:$EF,V} = AntiSpinor{V}(a.v*b)
+        *(a::F,b::CoSpinor{V}) where {F<:$EF,V} = CoSpinor{V}(a*b.v)
+        *(a::CoSpinor{V},b::F) where {F<:$EF,V} = CoSpinor{V}(a.v*b)
         *(a::F,b::Chain{V,G}) where {F<:$EF,V,G} = Chain{V,G}(a*b.v)
         *(a::Chain{V,G},b::F) where {F<:$EF,V,G} = Chain{V,G}(a.v*b)
         *(a::F,b::Single{V,G,B,T} where B) where {F<:$EF,V,G,T} = Single{V,G}($Sym.:∏(a,b.v),basis(b))
@@ -1087,12 +1087,12 @@ function generate_products(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj
                 return Spinor{V}(out)=#
                 return Spinor{V}($(bcast(bop,:(a.v,b.v))))
             end
-            function $po(a::AntiSpinor{V,T},b::AntiSpinor{V,S}) where {V,T<:$Field,S<:$Field}
+            function $po(a::CoSpinor{V,T},b::CoSpinor{V,S}) where {V,T<:$Field,S<:$Field}
                 #=$(insert_expr((:N,:t),VEC)...)
                 out = value(a,$VECS(N,t))
                 $(add_val(eop,:out,:(value(b,$VECS(N,t))),bop))
-                return AntiSpinor{V}(out)=#
-                return AntiSpinor{V}($(bcast(bop,:(a.v,b.v))))
+                return CoSpinor{V}(out)=#
+                return CoSpinor{V}($(bcast(bop,:(a.v,b.v))))
             end
             function $po(a::Spinor{V,T},b::Multivector{V,S}) where {V,T<:$Field,S<:$Field}
                 return $po(Multivector{V}(a),b)
@@ -1100,10 +1100,10 @@ function generate_products(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj
             function $po(a::Multivector{V,T},b::Spinor{V,S}) where {V,T<:$Field,S<:$Field}
                 return $po(a,Multivector{V}(b))
             end
-            function $po(a::AntiSpinor{V,T},b::Multivector{V,S}) where {V,T<:$Field,S<:$Field}
+            function $po(a::CoSpinor{V,T},b::Multivector{V,S}) where {V,T<:$Field,S<:$Field}
                 return $po(Multivector{V}(a),b)
             end
-            function $po(a::Multivector{V,T},b::AntiSpinor{V,S}) where {V,T<:$Field,S<:$Field}
+            function $po(a::Multivector{V,T},b::CoSpinor{V,S}) where {V,T<:$Field,S<:$Field}
                 return $po(a,Multivector{V}(b))
             end
             function $po(a::Chain{V,G,T},b::Spinor{V,S}) where {V,G,T<:$Field,S<:$Field}
@@ -1126,22 +1126,22 @@ function generate_products(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CONJ=:conj
                     return $po(Multivector{V}(a),b)
                 end
             end
-            function $po(a::Chain{V,G,T},b::AntiSpinor{V,S}) where {V,G,T<:$Field,S<:$Field}
+            function $po(a::Chain{V,G,T},b::CoSpinor{V,S}) where {V,G,T<:$Field,S<:$Field}
                 if isodd(G)
                     $(insert_expr((:N,:t,:rrr,:bng),VEC)...)
                     out = convert($VECS(N,t),$(bcast(bop,:(value(b,$VECS(N,t)),))))
                     @inbounds $(add_val(:(+=),:(out[list(rrr+1,rrr+bng)]),:(value(a,$VEC(N,G,t))),ADD))
-                    return AntiSpinor{V}(out)
+                    return CoSpinor{V}(out)
                 else
                     return $po(a,Multivector{V}(b))
                 end
             end
-            function $po(a::AntiSpinor{V,T},b::Chain{V,G,S}) where {V,T<:$Field,G,S<:$Field}
+            function $po(a::CoSpinor{V,T},b::Chain{V,G,S}) where {V,T<:$Field,G,S<:$Field}
                 if isodd(G)
                     $(insert_expr((:N,:t,:rrr,:bng),VEC)...)
                     out = value(a,$VECS(N,t))
                     @inbounds $(add_val(eop,:(out[list(rrr+1,rrr+bng)]),:(value(b,$VEC(N,G,t))),bop))
-                    return AntiSpinor{V}(out)
+                    return CoSpinor{V}(out)
                 else
                     return $po(Multivector{V}(a),b)
                 end
@@ -1223,13 +1223,13 @@ for (mop,product!,field) ∈ ((:∧,:exteraddmulti!,false),(:⟑,:geomaddmulti!,
             loop = generate_loop_m_s(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
             product_loop(V,:Multivector,loop,VEC)
         end
-        @generated function $op(a::AntiSpinor{V,T},b::Multivector{V,S},$(args...)) where {V,T,S}
+        @generated function $op(a::CoSpinor{V,T},b::Multivector{V,S},$(args...)) where {V,T,S}
             $indu
             MUL,VEC = mulvec(a,b)
             loop = generate_loop_a_m(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
             product_loop(V,:Multivector,loop,VEC)
         end
-        @generated function $op(a::Multivector{V,T},b::AntiSpinor{V,S},$(args...)) where {V,T,S}
+        @generated function $op(a::Multivector{V,T},b::CoSpinor{V,S},$(args...)) where {V,T,S}
             $indu
             MUL,VEC = mulvec(a,b)
             loop = generate_loop_m_a(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
@@ -1254,11 +1254,11 @@ for (mop,product!,field) ∈ ((:∧,:exteraddspin!,false),(:⟑,:geomaddspin!,fa
             $indu
             Grassmann.$prop(a,b,false,$field)
         end
-        @generated function $op(b::AntiSpinor{V,T},a::TensorGraded{V,G},$(args...)) where {V,T,G}
+        @generated function $op(b::CoSpinor{V,T},a::TensorGraded{V,G},$(args...)) where {V,T,G}
             $indu
             Grassmann.$prop(a,b,true,$field)
         end
-        @generated function $op(a::TensorGraded{V,G},b::AntiSpinor{V,S},$(args...)) where {V,G,S}
+        @generated function $op(a::TensorGraded{V,G},b::CoSpinor{V,S},$(args...)) where {V,G,S}
             $indu
             Grassmann.$prop(a,b,false,$field)
         end
@@ -1277,7 +1277,7 @@ for (mop,product!,field) ∈ ((:∧,:exteraddspin!,false),(:⟑,:geomaddspin!,fa
             loop = generate_loop_spinor(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
             product_loop(V,:Spinor,loop,Symbol(string(VEC)*"s"))
         end
-        @generated function $op(a::AntiSpinor{V,T},b::AntiSpinor{V,S},$(args...)) where {V,T,S}
+        @generated function $op(a::CoSpinor{V,T},b::CoSpinor{V,S},$(args...)) where {V,T,S}
             $indu
             MUL,VEC = mulvec(a,b)
             loop = generate_loop_anti(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
@@ -1292,39 +1292,39 @@ for (mop,product!,field) ∈ ((:∧,:exteraddanti!,false),(:⟑,:geomaddanti!,fa
     args = field ? (:g,) : ()
     indu = field ? :(isinduced(g) && (return :($$mop(a,b)))) : nothing
     @eval begin
-        @generated function $op(a::Spinor{V,T},b::AntiSpinor{V,S},$(args...)) where {V,T,S}
+        @generated function $op(a::Spinor{V,T},b::CoSpinor{V,S},$(args...)) where {V,T,S}
             $indu
             MUL,VEC = mulvec(a,b)
             loop = generate_loop_s_a(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
-            product_loop(V,:AntiSpinor,loop,Symbol(string(VEC)*"s"))
+            product_loop(V,:CoSpinor,loop,Symbol(string(VEC)*"s"))
         end
-        @generated function $op(a::AntiSpinor{V,T},b::Spinor{V,S},$(args...)) where {V,T,S}
+        @generated function $op(a::CoSpinor{V,T},b::Spinor{V,S},$(args...)) where {V,T,S}
             $indu
             MUL,VEC = mulvec(a,b)
             loop = generate_loop_a_s(V,:(a.v),:(b.v),promote_type(T,S),MUL,$product!,$preproduct!,$field)
-            product_loop(V,:AntiSpinor,loop,Symbol(string(VEC)*"s"))
+            product_loop(V,:CoSpinor,loop,Symbol(string(VEC)*"s"))
         end
     end
 end
 @generated function ∨(a::Spinor{V,T},b::Spinor{V,S}) where {V,T,S}
     MUL,VEC = mulvec(a,b)
     loop = generate_loop_spinor(V,:(a.v),:(b.v),promote_type(T,S),MUL,isodd(mdims(V)) ? meetaddanti! : meetaddspin!,isodd(mdims(V)) ? meetaddanti!_pre : meetaddspin!_pre)
-    product_loop(V,isodd(mdims(V)) ? :AntiSpinor : :Spinor,loop,Symbol(string(VEC)*"s"))
+    product_loop(V,isodd(mdims(V)) ? :CoSpinor : :Spinor,loop,Symbol(string(VEC)*"s"))
 end
-@generated function ∨(a::AntiSpinor{V,T},b::AntiSpinor{V,S}) where {V,T,S}
+@generated function ∨(a::CoSpinor{V,T},b::CoSpinor{V,S}) where {V,T,S}
     MUL,VEC = mulvec(a,b)
     loop = generate_loop_anti(V,:(a.v),:(b.v),promote_type(T,S),MUL,isodd(mdims(V)) ? meetaddanti! : meetaddspin!,isodd(mdims(V)) ? meetaddanti!_pre : meetaddspin!_pre)
-    product_loop(V,isodd(mdims(V)) ? :AntiSpinor : :Spinor,loop,Symbol(string(VEC)*"s"))
+    product_loop(V,isodd(mdims(V)) ? :CoSpinor : :Spinor,loop,Symbol(string(VEC)*"s"))
 end
-@generated function ∨(a::Spinor{V,T},b::AntiSpinor{V,S}) where {V,T,S}
+@generated function ∨(a::Spinor{V,T},b::CoSpinor{V,S}) where {V,T,S}
     MUL,VEC = mulvec(a,b)
     loop = generate_loop_s_a(V,:(a.v),:(b.v),promote_type(T,S),MUL,isodd(mdims(V)) ? meetaddspin! : meetaddanti!,isodd(mdims(V)) ? meetaddspin!_pre : meetaddanti!_pre)
-    product_loop(V,isodd(mdims(V)) ? :Spinor : :AntiSpinor,loop,Symbol(string(VEC)*"s"))
+    product_loop(V,isodd(mdims(V)) ? :Spinor : :CoSpinor,loop,Symbol(string(VEC)*"s"))
 end
-@generated function ∨(a::AntiSpinor{V,T},b::Spinor{V,S}) where {V,T,S}
+@generated function ∨(a::CoSpinor{V,T},b::Spinor{V,S}) where {V,T,S}
     MUL,VEC = mulvec(a,b)
     loop = generate_loop_a_s(V,:(a.v),:(b.v),promote_type(T,S),MUL,isodd(mdims(V)) ? meetaddspin! : meetaddanti!,isodd(mdims(V)) ? meetaddspin!_pre : meetaddanti!_pre)
-    product_loop(V,isodd(mdims(V)) ? :Spinor : :AntiSpinor,loop,Symbol(string(VEC)*"s"))
+    product_loop(V,isodd(mdims(V)) ? :Spinor : :CoSpinor,loop,Symbol(string(VEC)*"s"))
 end
 
 for side ∈ (:left,:right)
@@ -1429,7 +1429,7 @@ for side ∈ (:left,:right)
                             @inbounds (isodd(N) ? setanti!_pre : setspin!_pre)(out,v,complement(N,ibi,D),Val{N}())
                         end
                     end
-                    return :($(isodd(N) ? :AntiSpinor : :Spinor){V}($(Expr(:call,tvecs(N,T),out...))))
+                    return :($(isodd(N) ? :CoSpinor : :Spinor){V}($(Expr(:call,tvecs(N,T),out...))))
                 else return quote
                     $(insert_expr((:N,:rs,:bn),:svec)...)
                     #P = $(c≠h ? 0 : :(hasinf(V)+hasorigin(V)))
@@ -1446,10 +1446,10 @@ for side ∈ (:left,:right)
                             end
                         end
                     end
-                    return $(isodd(N) ? :AntiSpinor : :Spinor){V}(out)
+                    return $(isodd(N) ? :CoSpinor : :Spinor){V}(out)
                 end end
             end
-            @generated function $c(m::AntiSpinor{V,T},$(args...)) where {V,T}
+            @generated function $c(m::CoSpinor{V,T},$(args...)) where {V,T}
                 isdyadic(V) && throw(error("Complement for dyadic tensors is undefined"))
                 $(c≠h ? nothing : :(((!isdiag(V)) || ($ff && !isinduced(g))) && (return :($$cc(metric(m,$($args...))))) ))
                 SUB,VEC = subvecs(m)
@@ -1467,7 +1467,7 @@ for side ∈ (:left,:right)
                             @inbounds (isodd(N) ? setspin!_pre : setanti!_pre)(out,v,complement(N,ibi,D),Val{N}())
                         end
                     end
-                    return :($(isodd(N) ? :Spinor : :AntiSpinor){V}($(Expr(:call,tvecs(N,T),out...))))
+                    return :($(isodd(N) ? :Spinor : :CoSpinor){V}($(Expr(:call,tvecs(N,T),out...))))
                 else return quote
                     $(insert_expr((:N,:ps,:bn),:svec)...)
                     #P = $(c≠h ? 0 : :(hasinf(V)+hasorigin(V)))
@@ -1484,7 +1484,7 @@ for side ∈ (:left,:right)
                             end
                         end
                     end
-                    return $(isodd(N) ? :Spinor : :AntiSpinor){V}(out)
+                    return $(isodd(N) ? :Spinor : :CoSpinor){V}(out)
                 end end
             end
         end
@@ -1506,7 +1506,7 @@ for c ∈ (:even,:odd)
                         @inbounds $(anti ? :setanti!_pre : :setspin!_pre)(out,v,ibi,Val{N}())
                     end
                 end
-                return :($$(anti ? :AntiSpinor : :Spinor){V}($(Expr(:call,tvecs(N,T),out...))))
+                return :($$(anti ? :CoSpinor : :Spinor){V}($(Expr(:call,tvecs(N,T),out...))))
             else return quote
                 $(insert_expr((:N,:bs,:bn),:svecs)...)
                 out = zeros($VEC(N,T))
@@ -1520,14 +1520,14 @@ for c ∈ (:even,:odd)
                         end
                     end
                 end
-                return $(anti ? :AntiSpinor : :Spinor){V}(out)
+                return $(anti ? :CoSpinor : :Spinor){V}(out)
             end end
         end
     end
 end
 for (side,field) ∈ ((:metric,false),(:anti,false),(:metric,true),(:anti,true))
     c,p = (side≠:anti ? side : Symbol(side,:metric)),Symbol(:parity,side)
-    tens,tensfull = Symbol(side,:tensor),Symbol(side,:full)
+    tens,tensfull = Symbol(side,:tensor),Symbol(side,:extensor)
     tenseven,tensodd = Symbol(side,:even),Symbol(side,:odd)
     args = field ? (:g,) : ()
     @eval begin
@@ -1664,7 +1664,7 @@ for (side,field) ∈ ((:metric,false),(:anti,false),(:metric,true),(:anti,true))
                 return Spinor{V}(out)
             end end
         end
-        @generated function $c(m::AntiSpinor{V,T},$(args...)) where {V,T}
+        @generated function $c(m::CoSpinor{V,T},$(args...)) where {V,T}
             isdyadic(V) && throw(error("Complement for dyadic tensors is undefined"))
             ($field && !isinduced(g)) && (return :(contraction(g,m)))
             (!isdiag(V)) && (return :(contraction($($tensodd(V)),m,)))
@@ -1686,7 +1686,7 @@ for (side,field) ∈ ((:metric,false),(:anti,false),(:metric,true),(:anti,true))
                         @inbounds setanti!_pre(out,v,ibi,Val{N}())
                     end
                 end
-                return :(AntiSpinor{V}($(Expr(:call,tvecs(N,T),out...))))
+                return :(CoSpinor{V}($(Expr(:call,tvecs(N,T),out...))))
             else return quote
                 $(insert_expr((:N,:ps,:bn),:svecs)...)
                 out = zeros($VEC(N,T))
@@ -1706,7 +1706,7 @@ for (side,field) ∈ ((:metric,false),(:anti,false),(:metric,true),(:anti,true))
                         end
                     end
                 end
-                return AntiSpinor{V}(out)
+                return CoSpinor{V}(out)
             end end
         end
     end
@@ -1832,7 +1832,7 @@ for reverse ∈ (:reverse,:involute,:conj,:clifford,:antireverse)
                 return Spinor{V}(out)
             end end
         end
-        @generated function $reverse(m::AntiSpinor{V,T}) where {V,T}
+        @generated function $reverse(m::CoSpinor{V,T}) where {V,T}
             if mdims(V)<cache_limit
                 $(insert_expr((:N,:ps,:bn,:D),:svecs)...)
                 out = svecs(N,Any)(zeros(svecs(N,T)))
@@ -1849,7 +1849,7 @@ for reverse ∈ (:reverse,:involute,:conj,:clifford,:antireverse)
                         end
                     end
                 end
-                return :(AntiSpinor{V}($(Expr(:call,tvecs(N,T),out...))))
+                return :(CoSpinor{V}($(Expr(:call,tvecs(N,T),out...))))
             else return quote
                 $(insert_expr((:N,:ps,:bn,:D),:svecs)...)
                 out = zeros($VECS(N,T))
@@ -1866,7 +1866,7 @@ for reverse ∈ (:reverse,:involute,:conj,:clifford,:antireverse)
                         end
                     end
                 end
-                return AntiSpinor{V}(out)
+                return CoSpinor{V}(out)
             end end
         end
     end