Re: what does 'mpoles' function do ? (what is 'poles' in it ?)

[Ben Abbott]

On Jun 25, 2011, at 5:13 PM, Sergei Steshenko wrote:

> Hello,
> 
> 'mpoles' function (http://octave.sourceforge.net/octave/function/mpoles.html)
> can be found under "Finding Roots" - see
> http://octave.sourceforge.net/octave/overview.html .
> 
> So, because of the "Finding Roots" I _guess_ the function deals with _roots_.
> 
> However, the description talks about poles.
> 
> I studied math and calculus quite a time ago, so I could easily forget what
> it's all about. AFAIR, if we have a
> 
> numerator / denominator
> 
> expression, and both numerator and denominator are polynomials, then
> roots of numerator are called zeros and roots of denominator are called
> poles. But both zeros and poles are related to the whole expression.
> 
> But other than that I do not know what poles have to do with polynomials.
> 
> Could anybody please clarify regarding 'mpoles' and poles it deals with ?
> 
> Thanks,
>  Sergei.

You're inference is correct.

mpoles() is used by the residue() function to identify a multiplicity of poles 
for A(z)/B(z).

Ben