Re: Re: Weird result in Mathematica 6

*To*: mathgroup at smc.vnet.net*Subject*: [mg76573] Re: [mg76431] Re: [mg76393] Weird result in Mathematica 6*From*: DrMajorBob <drmajorbob at bigfoot.com>*Date*: Thu, 24 May 2007 06:02:43 -0400 (EDT)*References*: <26727995.1179743868970.JavaMail.root@m35> <200705220647.CAA19795@smc.vnet.net> <9745176.1179921476358.JavaMail.root@m35> <op.tssgfzliqu6oor@monster.ma.dl.cox.net> <4431163.1179955154502.JavaMail.root@m35>*Reply-to*: drmajorbob at bigfoot.com

$Version "6.0 for Microsoft Windows (32-bit) (April 20, 2007)" Bobby On Wed, 23 May 2007 16:17:31 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl> wrote: > Yes, its curious. It might just be "platform dependence" but is more > likely to be "time of release dependence". Mine is: > > > $Version > > "6.0 for Mac OS X PowerPC (32-bit) (April 20, 2007)" > > Andrzej > > > On 24 May 2007, at 01:37, DrMajorBob wrote: > >> 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 > > -- DrMajorBob at bigfoot.com

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