finalized mixed-symmetry algebra dispatch

README.md

@@ -353,7 +353,7 @@ x * y + (dy * x + dx * y)v₁ϵ₁
 ```
 Higher order and multivariable Taylor numbers are also supported.
 ```Julia
-julia> @basis tangent(ℝ,2,2)
+julia> @basis tangent(ℝ,2,2) # 1D Grade, 2nd Order, 2 Variables
 (⟨+₁₂⟩, v, v₁, ∂₁, ∂₂, ∂₁v₁, ∂₂v₁, ∂₁₂, ∂₁₂v₁)
 
 julia> ∂1 * ∂1v1
@@ -365,20 +365,21 @@ julia> ∂1 * ∂2
 julia> v1*∂12
 ∂₁₂v₁
 
-julia> ∂12*∂2
+julia> ∂12*∂2 # 3rd order is zero
 0v
-```
-Although the implementation in this release is still experimental.
-```Julia
-julia> @mixedbasis tangent(ℝ^2,2,2);
 
-julia> SChain{Any,V,2}([0,1,0,0,1,0])
+julia> @mixedbasis tangent(ℝ^2,2,2); # 2D Grade, 2nd Order, 2 Variables
+
+julia> ∇ = ∂1v1 + ∂2v2 # vector field
 0v₁₂ + 1∂₁v₁ + 0∂₂v₁ + 0∂₁v₂ + 1∂₂v₂ + 0∂₁₂
 
-julia> ans^2
-0.0 + 1.0∂₁∂₁ + 1.0∂₂∂₂
+julia> ∇ ⋅ ∇ # Laplacian
+0.0v₁ + 0.0v₂ + 1∂₁∂₁ + 1∂₂∂₂
+
+julia> ans*∂1 # 3rd order is zero
+0.0v⃖
 ```
-For example, a constructor with explicit `Any` type delcaration must be used to be able to properly work with nested symmetric Leibniz basis elements. If the `StaticArray` type is not set to `Any` currently, the type system is incompatible.
+Although fully generalized, the implementation in this release is still experimental.
 
 ## Constructing linear transformations from mixed tensor product ⊗
 

src/algebra.jl

@@ -50,9 +50,8 @@ function declare_mutating_operations(M,F,set_val,SUB,MUL)
                     if v ≠ 0 && !diffcheck(V,a,b)
                         A,B,Q,Z = symmetricmask(V,a,b)
                         val = (typeof(V)<:Signature || count_ones(A&B)==0) ? (parity(A,B,V) ? $SUB(v) : v) : $MUL(parityinner(A,B,V),v)
-                        if diffvars(V)≠0 && !iszero(Z)
-                            T≠Any && (return true)
-                            val *= getbasis(V,Z)
+                        if diffvars(V)≠0
+                            !iszero(Z) && (T≠Any ? (return true) : (val *= getbasis(V,Z)))
                             count_ones(Q)+order(val)>diffmode(V) && (return false)
                         end
                         $s(m,val,(A⊻B)|Q,Dimension{N}())
@@ -64,9 +63,8 @@ function declare_mutating_operations(M,F,set_val,SUB,MUL)
                         A,B,Q,Z = symmetricmask(V,a,b)
                         pcc,bas,cc = (hasinf(V) && hasorigin(V)) ? conformal(A,B,V) : (false,A⊻B,false)
                         val = (typeof(V)<:Signature || count_ones(A&B)==0) ? (parity(A,B,V)⊻pcc ? $SUB(v) : v) : $MUL(parityinner(A,B,V),pcc ? $SUB(v) : v)
-                        if diffvars(V)≠0 && !iszero(Z)
-                            T≠Any && (return true)
-                            val *= getbasis(V,Z)
+                        if diffvars(V)≠0
+                            !iszero(Z) && (T≠Any ? (return true) : (val *= getbasis(V,Z)))
                             count_ones(Q)+order(val)>diffmode(V) && (return false)
                         end
                         $s(m,val,bas|Q,Dimension{N}())
@@ -86,10 +84,12 @@ function declare_mutating_operations(M,F,set_val,SUB,MUL)
                         if val ≠ 0
                             g,C,t,Z = $uct(A,B,V)
                             v = val
-                            if diffvars(V)≠0 && !iszero(Z)
-                                T≠Any && (return true)
-                                _,_,Q,_ = symmetricmask(V,A,B)
-                                v *= getbasis(V,Z)
+                            if diffvars(V)≠0
+                                if !iszero(Z)
+                                    T≠Any && (return true)
+                                    _,_,Q,_ = symmetricmask(V,A,B)
+                                    v *= getbasis(V,Z)
+                                end
                                 count_ones(Q)+order(v)>diffmode(V) && (return false)
                             end
                             t && $s(m,typeof(V) <: Signature ? g ? $SUB(v) : v : $MUL(g,v),C,Dimension{N}())
@@ -483,9 +483,11 @@ function generate_product_algebra(Field=Field,VEC=:mvec,MUL=:*,ADD=:+,SUB=:-,CON
                 g,C,f,Z = interior(α,β,V)
                 !iszero(C) && T≠Any && (return true)
                 v = iszero(C) ? γ : γ*getbasis(V,C)
-                if diffvars(V)≠0 && !iszero(Z)
-                    _,_,Q,_ = symmetricmask(V,α,β)
-                    v *= getbasis(V,Z)
+                if diffvars(V)≠0
+                    if !iszero(Z)
+                        _,_,Q,_ = symmetricmask(V,α,β)
+                        v *= getbasis(V,Z)
+                    end
                     order(v)>diffmode(V) && (return false)
                 end
                 f && (mv.v = typeof(V)<:Signature ? (g ? $SUB(mv.v,v) : $ADD(mv.v,v)) : $ADD(mv.v,$MUL(g,v)))

src/utilities.jl

@@ -159,7 +159,7 @@ Base.@pure promote_type(t...) = Base.promote_type(t...)
     assign_expr!(e,x,:N,:(ndims(V)))
     assign_expr!(e,x,:M,:(Int(N/2)))
     assign_expr!(e,x,:t,vec≠:mvec ? :Any : :(promote_type($T,$S)))
-    assign_expr!(e,x,:out,mv≠0 ? :(t=Any;zeros(svec(N,Any)).+out) : :(zeros($vec(N,t))))
+    assign_expr!(e,x,:out,mv≠0 ? :(t=Any;convert(svec(N,Any),out)) : :(zeros($vec(N,t))))
     assign_expr!(e,x,:mv,:(MBlade{V,0,getbasis(V,0),$(mv≠0 ? Any : :t)}($mv)))
     assign_expr!(e,x,:r,:(binomsum(N,G)))
     assign_expr!(e,x,:bng,:(binomial(N,G)))