compare only real components with ==. closes #10

README.md

@@ -20,7 +20,7 @@ imaginary part represents the fermionic direction), in screw theory, in motor
 and spatial vector algebra, and in computer science due to its relation with the 
 forward mode of automatic differentiation.
 
-The `ForwardDiff` package implements forward mode automatic differentiation in Julia using several approaches. One
+The [ForwardDiff](https://github.com/scidom/ForwardDiff.jl) package implements forward mode automatic differentiation in Julia using several approaches. One
 of these approaches employs dual numbers. For this reason, the `ForwardDiff` package relies on `DualNumbers`. The
 user is referred to `ForwardDiff` for some examples on how to perform forward mode automatic differentiation using
 dual numbers in Julia.
@@ -49,6 +49,10 @@ numerical derivatives, for example, ``conj``, ``abs`` and ``abs2``. In these
 cases, we choose to follow the rule ``f(x::Dual) = Dual(f(real(x)),epsilon(x)*f'(real(x)))``,
 where ``f'`` is the derivative of ``f``. The mathematical definitions are
 available using the functions with the suffix ``dual``.
+Similarly, comparison operators ``<``, ``>``, and ``==`` are overloaded to compare only real
+components.
+
+
 
 
 ### A walk-through example

src/dual.jl

@@ -96,7 +96,7 @@ end
 convert(::Type{Dual}, z::Dual) = z
 convert(::Type{Dual}, x::Real) = dual(x)
 
-==(z::Dual, w::Dual) = real(z) == real(w) && epsilon(z) == epsilon(w)
+==(z::Dual, w::Dual) = real(z) == real(w)
 # ==(z::Dual, x::Real) = real_valued(z) && real(z) == x
 # ==(x::Real, z::Dual) = real_valued(z) && real(z) == x