Override Base.sum! (#368)

* Override Base.sum!

* Suggestion by @lbenet

src/TaylorSeries.jl

@@ -40,7 +40,7 @@ import Base: iterate, size, eachindex, firstindex, lastindex,
     eltype, length, getindex, setindex!, axes, copyto!
 
 import Base: zero, one, zeros, ones, isinf, isnan, iszero, isless,
-    convert, promote_rule, promote, show,
+    convert, promote_rule, promote, show, sum!,
     real, imag, conj, adjoint,
     rem, mod, mod2pi, abs, abs2,
     sqrt, exp, expm1, log, log1p,

src/arithmetic.jl

@@ -405,6 +405,27 @@ for (f, fc) in ((:+, :(add!)), (:-, :(subst!)))
     end
 end
 
+for T in (:Taylor1, :TaylorN)
+    @eval begin
+        function sum!(v::$T{S}, a::AbstractArray{$T{S}}) where {S <: Number}
+            for i in eachindex(a)
+                for k in eachindex(v)
+                    add!(v, v, a[i], k)
+                end
+            end
+            return nothing
+        end
+    end
+end
+
+function sum!(v::TaylorN{S}, a::AbstractArray{HomogeneousPolynomial{S}}) where {S <: Number}
+    for i in eachindex(a)
+        for k in eachindex(v)
+            add!(v, v, a[i], k)
+        end
+    end
+    return nothing
+end
 
 ## Multiplication ##
 for T in (:Taylor1, :HomogeneousPolynomial, :TaylorN)