Re: ideas please!
- To: mathgroup at smc.vnet.net
- Subject: [mg78877] Re: ideas please!
- From: dh <dh at metrohm.ch>
- Date: Thu, 12 Jul 2007 05:08:19 -0400 (EDT)
- References: <f72b1b$8cj$1@smc.vnet.net>
Hi Dimitris,
no, the imaginary part does not have a discontinuity. Log is a
multivalued function: Log[Abs[x]]+I Arg[x]+I n 2 Pi and Mathematica has to
choose a value (principal value). It does this by choosing the value
(branch) which has an imaginary part between -Pi and Pi. Therefore, the
"jump" happens where the function argument of Log is negative real,
where its imaginary part is zero. Further, you want the positive
value,therefore:
t= function argument of Log;
Reduce[{Im[t] == 0, z > 0}, z]
this gives y root object. If you want y machine number, use N.
hope this helps, Daniel
dimitris wrote:
> Hello.
>
> In[201]:=
> (Plot[#1[Log[1 - (I + z)/((-(1/3) + I) + (1/6)*(1 +
> I*Sqrt[3])*((1/2)*(29 - 3*Sqrt[93]))^(1/3) +
> (1 - I*Sqrt[3])/(3*2^(2/3)*(29 - 3*Sqrt[93])^(1/3)))]], {z,
> 0, 5}] & ) /@ {Re, Im};
>
> As it is clear from the graph the Imaginary part has a jump
> discontinuity somewhere near z=1.
> Can somebody point me out a way to detect exactly its position?
> No matter what I have tried I had no success.
>
> Dimitris
>
>