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MathGroup Archive 2007

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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


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