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Re: using FindRoot to find multiple answers in a domain?

  • To: mathgroup at
  • Subject: [mg69261] Re: using FindRoot to find multiple answers in a domain?
  • From: Paul Abbott <paul at>
  • Date: Mon, 4 Sep 2006 02:41:25 -0400 (EDT)
  • Organization: The University of Western Australia
  • References: <ed0rn9$sm6$> <ed3rou$rv5$>
  • Sender: owner-wri-mathgroup at

In article <ed3rou$rv5$1 at>, "akil" <akomur at> 

> IntervalRoots package and RootSearch do not work for the kind of formulas I 
> have.

Are you sure?

> For example in the domain [0,Pi/2] we want to solve (I only used FindRoot 
> because this was the fastest):
> I put the package I test in on 
> so that you can see the 
> formulas I use.
> Copying them In here ruins the formulas.

Copy as Plain text. Your first formula is

  nlv = Max[-81.24275115593154  Cot[beta] - 48.489352280270914,   
        Min[-46.844746272761526 Cot[beta] - 71.4213555357176, 
            -46.480384751324436 Cot[beta] - 71.66426321667566]]

Note that PiecewiseExpand can be applied to such formulae. If you 
simplify the result


you deduce that nlv is just

  -81.24275115593154  Cot[beta] - 48.489352280270914 if Cot[beta] <= 2/3

  -46.844746272761526 Cot[beta] - 71.4213555357176 if Cot[beta] >= 2/3

You can check that these values are consistent when Cot[beta] == 2/3. 
Moreover, the catch-all condition

  -46.480384751324436 Cot[beta] - 71.66426321667566

is redundant for real beta since it only applies when Cot[beta] == 2/3. 
A brief examination of nuvb shows that it involves ratios of (powers of) 
expressions similar to nlv. I expect that simplification of these 
expressions prior to constructing nuvb would lead to a final form that 
is not that hard to handle.

I expect that if you step back and tell us more about the original 
problem, then a more elegant approach would present itself.


Paul Abbott                                      Phone:  61 8 6488 2734
School of Physics, M013                            Fax: +61 8 6488 1014
The University of Western Australia         (CRICOS Provider No 00126G)    

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