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Re: FindRoots?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg112192] Re: FindRoots?
  • From: Syd Geraghty <sydgeraghty at me.com>
  • Date: Sat, 4 Sep 2010 04:00:13 -0400 (EDT)

Gianluca,

Wolfram has evidently fixed the 1st problem you mentioned.

Reduce[2 x+Log[-((-1+2 x)/(-1+2 x^2))]==0 && -2 < x<-1/Sqrt[2],x,Reals]

x==Root[{Log[-((-1+2 #1)/(-1+2 #1^2))]+2 #1&,-0.86193624643066461860}]

Yours truly ... Syd Geraghty

Syd Geraghty B.Sc., M.Sc.
sydgeraghty at me.com
San Jose, CA

Mathematica 7.0.1.0 for Mac OS X x86 (64 - bit) (12 September 2009)  
Licenses: L2983-5890, L3028-2592
MacOS X V 10.6.1 Snow Leopard
MacBook Pro 2.33 Ghz Intel Core 2 Duo  2GB RAM

On Sep 3, 2010, at 3:10 AM, Gianluca Gorni wrote:

> In my opinion Reduce can replace RootSearch in some
> cases but not in others.
> 
> First of all, Reduce has bugs. Here is an analytic function
> that clearly has a real root:
> 
> Plot[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))], {x, -2, -1/Sqrt[2]}]
> 
> Still, Reduce does not see it (as of version 7.0.1):
> 
> Reduce[2 x + Log[-((-1 + 2 x)/(-1 + 2 x^2))] ==== 0 && -2 <
>   x < -1/Sqrt[2], x, Reals]
> False
> 
> (I reported this example to wolfram last year).



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