Re: Abs[x] function

*To*: mathgroup at smc.vnet.net*Subject*: [mg87849] Re: Abs[x] function*From*: dh <dh at metrohm.ch>*Date*: Fri, 18 Apr 2008 07:11:11 -0400 (EDT)*References*: <fu9fn7$c8d$1@smc.vnet.net>

Hi Vlad, by default Mathematica uses complex numbers. As Abs is not an analytical function, it does not have a derivative (the differential quotient depends on direction). Therefore, the derivative of Abs is not defined. For your application, you could define the derivative you would like to have yourself by e.g.: Unprotect[Abs]; Abs'[x_]:=Which[x<0,-1,x==0,"undefined",x>0,1]; hope this helps, Daniel Vladislav wrote: > Who can explain the behavior. THe derivative Abs[x] at x=.5 is well > defined and is equal to 1. > > In[1]:= D[Abs[x], x] > > Out[1]= > \!\(\*SuperscriptBox["Abs", "\[Prime]", > MultilineFunction->None]\)[x] > > In[2]:= % /. x -> .5 > > Out[2]= > \!\(\*SuperscriptBox["Abs", "\[Prime]", > MultilineFunction->None]\)[0.5] >