Re: Real/Comlex function problem with D
- To: mathgroup at smc.vnet.net
- Subject: [mg74226] Re: Real/Comlex function problem with D
- From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
- Date: Thu, 15 Mar 2007 04:54:45 -0500 (EST)
- Organization: The Open University, Milton Keynes, UK
- References: <et8e29$pqb$1@smc.vnet.net>
bar at ANTYSPAM.ap.krakow.pl wrote:
> Hi,
> I have a complex function F[x]
> When i defined:
> ff[x_]:=Arg[F[x]] (* i tried ComplexExpand[Arg[F[x]]] too *)
>
> I obtainned good Plot[ff[x]] - its real - (no complex)
>
> When i try
> ff1[x_]:=D[ff[x],x];
> I found ff1 is Complex funtion again !!
>
> Why ?
>
> (i tried Evaluate; Element[x,Reals]; FullSimplify - always the same)
>
> Regards, Olaf
>
>
Hi Olaf,
You might get better results by using ArcTan rather than Arg since
Mathematica does not know how to differentiate Arg. (Note that ArcTan
returns values between -Pi/2 and Pi/2, whereas Arg returns values
between -Pi and Pi.) Compare
In[1]:=
ff[x_] := Arg[F[x]]
ff1[x_] := D[ff[x], x]
ff1[x]
Out[3]=
Arg'[F[x]] F'[x]
with
In[4]:=
ff[x_] := ArcTan[F[x]]
ff1[x_] := D[ff[x], x]
ff1[x]
Out[6]=
F'[x]
---------
2
1 + F[x]
Regards,
Jean-Marc