plotting modulus of complex function



On 05/03/2012 03:26 PM, Jaime Villate wrote:
>
> Hi,
> the function used to obtain the modulus of a complex number is cabs()
> and not abs(). However, in the command plot2d(float(abs(Ge(s))), [s,
> 1e-1, 1e3]) cabs would give you a very long expression in terms of s
> which might get your system stuck. I suggest that you first compute the
> floating-point value for a given s,
> then compute cabs and only then pass the result. Also, the notation
> epsilon[0] might look cute in Wxmaxima,
> but it means defining an array which you really don't need and will add
> to the computational complexity.
> You might want to try something such as:
 >
 > [... snip code ...]
>
> Your functions have several steep spikes, so you might have to view separate
> parts of the frequency domain in separate plots, in order to see the
> separate spikes.
 > [...]

Hello Jaime (and list),

Thanks for the hints.  Actually, the main problem for me not being able 
to plot, appeared to be a problem with my gnuplot install.

The real reason why I wanted to look at the Ge(s) function is that I 
want to understand its behavior for s->0.  If I plot its modulus, i see 
a quite smooth behavior between 1e-7 and 1e-1, but for values lower than 
1e-7 the abs(Ge(s)) function seems to go up again???

So I'm in doubt... is lim_{s->0} Ge(s) = constant or infinity?  Is the 
'weird behavior' below 1e-8 just a result of rounding error, or could it 
really be that lim_{s->0} Ge(s) = infinity?  My educated guess is that 
it's rounding error and that the limit should indeed give me a constant 
value.

Calculating the limit analytically by hand turned out to be a mess and I 
gave up... If i try with Maxima, i can't get a result... the computation 
seems to take long and it gives up at the end.

Is there any Maxima-expert who can change my code so that the evaluation 
of lim_{s->0} Ge(s) gives me the constant value for the limit that I 
expect?  Preferably in parametric form, but a numerical value obtained 
with all the parameters filled in would also be nice.

My script, with some comments concerning the problem description, can be 
found at

https://www.dropbox.com/s/6ie4i31b1gi2nm1/bartscript.mac

Kind regards,
Bart