Argument of a Dual Number

[juliadiff]

Argument of a Dual Number

[dlfivefifty]

angle refers to the argument in the complex plane, and so the current definition is correct as the argument does not change if we perturb a real number by a small real ε perturbation. Two other examples:

angle(dual(im,im)) # returns π/2+0ε as the argument stays fixed
angle(dual(1,im)) # returns 0+ε as the argument changes

[dlfivefifty]

Your proposed angle could be implemented as a separate function DualNumbers.dualangle. Overriding Base.angle would be confusing in the context of complex numbers. This confusion is the reason that Base.real overrides were replaced with DualNumbers.realpart.