generalized (anti)-symmetrization formula

src/algebra.jl

@@ -261,11 +261,19 @@ function cross(a::X,b::Y) where {X<:TensorTerm{V},Y<:TensorTerm{V}} where V
     return SValue{V}(p ? -v : v,Basis{V}(C))
 end
 
-## commutator product
+# symmetrization and anti-symmetrization
 
-export ⨲
+export ⨰, ⨲
 
-⨲(a,b) = a*b - b*a
+⨰(x::T...) where T<:TensorAlgebra{V} where V = sum(x)/factorial(length(x))
+
+function ⨲(x::T...) where T<:TensorAlgebra{V} where V
+    K,P,out = length(x),collect(permutations(1:K)),x[1]
+    for n ∈ 2:K
+        DirectSum.indexparity!(P,V)[1] ? (out-=x[n]) : (out+=x[n])
+    end
+    return out/factorial(K)
+end
 
 ### Product Algebra Constructor