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Re: Real/Comlex function problem with D

• To: mathgroup at smc.vnet.net
• Subject: [mg74240] Re: Real/Comlex function problem with D
• From: dh <dh at metrohm.ch>
• Date: Thu, 15 Mar 2007 05:02:18 -0500 (EST)
• References: <et8e29$pqb$1@smc.vnet.net>

Hi,

Consider ff1[x_]:=D[ff[x],x]. Now f[3.] evaluates to D[ff[3]],3], hardly 

what you want.

Presumably your mean ff1[x]:=ff'[x]. But now we have the problem that we 

need the derivative of Abs and in general (in the complex field) this 

derivative is not defined. You could try to make a definition for 

Element[x,Reals], but you need to take care of branch cuts, that depend 

on your F.

What you can do is to approximate the real Arg[x] with real x by e.g. 

Interpolation or any other approximation metod like e.g.:, 

Calculus`Pade` , NumericalMath`Approximations` , NumericalMath`NSeries` 

, NumericalMath`PolynomialFit`

Daniel





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

> 

>