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).