refined DirectSum support and implemented @subtype macro

REQUIRE

@@ -1,4 +1,5 @@
 julia 0.7
 ForceImport
 SyntaxTree
+DirectSum
 AbstractTensors

src/Reduce.jl

@@ -105,10 +105,18 @@ include("switch.jl") # load switch operators
 
 module Algebra
 using Reduce, LinearAlgebra
+import ..extract
 
 include("unary.jl") # load unary operators
 include("args.jl") # load calculus operators
 
+function init_subtype(name)
+    Expr(:block,[:(Base.$i(r::$name...)=$i(extract.(r)...)|>$name) for i ∈ [alg;iops]]...) |> eval
+    Expr(:block,[:($i(r::$name...)=$i(extract.(r)...)|>$name) for i ∈ [calculus;cnan;cmat]]...) |> eval
+    Expr(:block,[:(Base.$i(r::$name)=$i(extract(r))|>$name) for i ∈ [sbas;[:length]]]...) |> eval
+    Expr(:block,[:($i(r::$name)=$i(extract(r))|>$name) for i ∈ [sfun;snan;snum;scom;sint;sran;smat]]...) |> eval
+end
+
 const variables = [
     :root_multiplicities,
     :requirements,
@@ -133,13 +141,22 @@ function bypass(op::Symbol,T::ExprSymbol,args)
     end
 end
 
-import AbstractTensors: TensorAlgebra
+import AbstractTensors: TensorAlgebra, value
+for op ∈ (:exp,:reverse)
+    bypass(op,:TensorAlgebra,(1,))
+end
 for op ∈ (:+,:-)
     bypass(op,:TensorAlgebra,(1,2))
 end
 for op ∈ (:*,:/)
     bypass(op,:TensorAlgebra,(2,))
 end
+abs(x::X) where X<:TensorAlgebra = sqrt(abs(value(LinearAlgebra.dot(x,x))))
+rank(x::X) where X<:TensorAlgebra = LinearAlgebra.rank(x)
+
+import DirectSum: SUB, PROD
+SUB(x::Expr) = -(x)
+PROD(x::AbstractVector{T}) where T<:Any = *(x...)
 
 @doc """
     ws()

src/rexpr.jl

@@ -136,6 +136,21 @@ function show(io::IO, ::MIME"text/latex", r::RExpr)
     print(io,"\n\\end{eqnarray}")
 end
 
+function extract end
+
+macro subtype(x)
+    x.head ≠ :<: && throw(error("$x is not a subtype expression"))
+    name = x.args[1]
+    Expr(:struct,false,x,Expr(:block,Expr(:(::), :r, :RExpr))) |> eval
+    @eval begin
+        export $name
+        show(io::IO, r::$name) = show(io,r.r)
+        extract(r::$name) = r.r
+        Algebra.init_subtype($name)
+    end
+    nothing
+end
+
 const r_to_jl = Dict(
     "i"             =>  "im",
     "infinity"      =>  "Inf"

src/unary.jl

@@ -24,7 +24,7 @@ const sbas = [
     :asinh,
     :atan,
     :atanh,
-    :atan2,
+    #:atan2,
     :cos,
     :cosh,
     :cot,
@@ -42,10 +42,10 @@ const sbas = [
     :sqrt,
     :tan,
     :tanh,
-    :gamma,
 ]
 
 const sdep = [
+    :gamma,
     :beta,
     :besseli,
     :besselj,