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Re: Re: Weird result in Mathematica 6

• To: mathgroup at smc.vnet.net
• Subject: [mg76559] Re: [mg76431] Re: [mg76393] Weird result in Mathematica 6
• From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
• Date: Thu, 24 May 2007 05:55:26 -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> <op.tsstz4blqu6oor@monster.ma.dl.cox.net>

That means definitely "platform dependence". It would be interesting 
if somone checked this on an Intel Mac. I think it is much more 
likely to be the processor than the operating system that makes the 
difference here. I don't know much about such things, but some 
processor specific libraries could be responsible for this.

Andrzej


On 24 May 2007, at 06:29, DrMajorBob wrote:

> $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,
>>>>>      x=B34}}];
>>>>> 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>