Change slicing to tail

Author: tansongchen

src/primitive.jl

@@ -5,9 +5,21 @@ import Base: asin, acos, atan, acot, asec, acsc, asinh, acosh, atanh, acoth, ase
 import Base: sinc, cosc
 import Base: +, -, *, /, \, ^, >, <, >=, <=, ==
 import Base: hypot, max, min
+import Base: zero, one, adjoint, conj, transpose
+
+using Base: tail
 
 # Unary
 
+@inline zero(::Type{TaylorScalar{T, N}}) where {T, N} = TaylorScalar{T, N}(zero(T))
+@inline one(::Type{TaylorScalar{T, N}}) where {T, N} = TaylorScalar{T, N}(one(T))
+@inline zero(::TaylorScalar{T, N}) where {T, N} = zero(TaylorScalar{T, N})
+@inline one(::TaylorScalar{T, N}) where {T, N} = one(TaylorScalar{T, N})
+
+transpose(t::TaylorScalar) = t
+adjoint(t::TaylorScalar) = t
+conj(t::TaylorScalar) = t
+
 ## Delegated
 
 @inline sqrt(t::TaylorScalar) = t^0.5
@@ -113,8 +125,12 @@ end
     ex = :($ex; TaylorScalar($([Symbol('v', i) for i in 1:N]...)))
     return :(@inbounds $ex)
 end
-@inline *(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1,T2,N} = *(promote(a,b)...)
-@inline /(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1,T2,N} = *(promote(a,b)...)
+@inline function *(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1, T2, N}
+    *(promote(a, b)...)
+end
+@inline function /(a::TaylorScalar{T1, N}, b::TaylorScalar{T2, N}) where {T1, T2, N}
+    *(promote(a, b)...)
+end
 
 for R in (Integer, Real)
     @eval @generated function ^(t::TaylorScalar{T, N}, n::S) where {S <: $R, T, N}

src/scalar.jl

@@ -1,5 +1,3 @@
-import Base: zero, one, adjoint, conj, transpose
-import Base: +, -, *, /
 import Base: convert, promote_rule
 
 export TaylorScalar
@@ -89,8 +87,9 @@ function promote_rule(::Type{TaylorScalar{T, N}},
         ::Type{S}) where {T, S, N}
     TaylorScalar{promote_type(T, S), N}
 end
-function promote_rule(::Type{TaylorScalar{T1, N}}, ::Type{TaylorScalar{T2,N}}) where {T1, T2, N}
-TaylorScalar{promote_type(T1,T2), N}
+function promote_rule(::Type{TaylorScalar{T1, N}},
+                      ::Type{TaylorScalar{T2, N}}) where {T1, T2, N}
+    TaylorScalar{promote_type(T1, T2), N}
 end
 
 function (::Type{F})(x::TaylorScalar{T, N}) where {T, N, F <: AbstractFloat}