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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>