Re: Re: Weird result in Mathematica 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg76566] Re: [mg76431] Re: [mg76393] Weird result in Mathematica 6*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Thu, 24 May 2007 05:59:05 -0400 (EDT)*References*: <26727995.1179743868970.JavaMail.root@m35> <200705220647.CAA19795@smc.vnet.net> <9745176.1179921476358.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

Interesting. But your results are entirely different from mine, for the same input. > which explains what is wrong (error messages can tell you a lot, > sometimes). And frequently, they don't. Here's the error message at THIS machine: FindRoot::lstol: The line search decreased the step size to within \ tolerance specified by AccuracyGoal and PrecisionGoal but was unable \ to find a sufficient decrease in the merit function. You may need \ more than MachinePrecision digits of working precision to meet these \ tolerances. >> Bobby On Tue, 22 May 2007 06:28:08 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > *This message was transferred with a trial version of CommuniGate(tm) > Pro* > I don't see any connection between these two issues. Moreover, I get: > > FindRoot[h == g, {x, 0}] > FindRoot::njnum:The Jacobian is not a matrix of numbers at {x} = {0.}. >> > {x -> 0.} > > which explains what is wrong (error messages can tell you a lot, > sometimes). Trying a slightly different starting search point: > > FindRoot[h == g, {x, 0.1}] > {x->2.} > > {g, h} /. % > {0., 0.} > > > Andrzej Kozlowski > > > On 22 May 2007, at 15:47, DrMajorBob wrote: > >> Even worse, FindRoot returns a wrong answer: >> >> g = Piecewise[{{0, x < 0}, {2 x - x^2, 0 <= x < 4}, {16 x - x^2, >> x³4}}]; >> h = x - 2; >> FindRoot[h == g, {x, 0}] >> {g, h} /. % >> >> {x->-2.84217*10^-15} >> {0, -2.} >> >> Bobby >> >> On Mon, 21 May 2007 05:01:21 -0500, Sebastian Meznaric >> <meznaric at gmail.com> wrote: >> >>> I was playing around with Mathematica 6 a bit and ran this command to >>> solve for the inverse of the Moebius transformation >>> >>> FullSimplify[ >>> Reduce[(z - a)/(1 - a\[Conjugate] z) == w && a a\[Conjugate] < 1 && >>> w w\[Conjugate] < 1, z]] >>> >>> This is what I got as a result: >>> -1 < w < 1 && -1 < a < 1 && z == (a + w)/(1 + w Conjugate[a]) >>> >>> Why is Mathematica assuming a and w are real? The Moebius >>> transformation is invertible in the unit disc regardless of whether a >>> and w are real or not. Any thoughts? >>> >>> >>> >> >> >> >> --DrMajorBob at bigfoot.com >> > > -- DrMajorBob at bigfoot.com

**References**:**Re: Weird result in Mathematica 6***From:*DrMajorBob <drmajorbob@bigfoot.com>