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Re: Re: Weird result in Mathematica 6
*To*: mathgroup at smc.vnet.net
*Subject*: [mg76574] Re: [mg76431] Re: [mg76393] Weird result in Mathematica 6
*From*: DrMajorBob <drmajorbob at bigfoot.com>
*Date*: Thu, 24 May 2007 06:03:14 -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> <23418457.1179976106322.JavaMail.root@m35>
*Reply-to*: drmajorbob at bigfoot.com
I'm using an AMD 3200+ processor, in case that matters.
Bobby
On Wed, 23 May 2007 16:37:54 -0500, Andrzej Kozlowski <akoz at mimuw.edu.pl>
wrote:
> *This message was transferred with a trial version of CommuniGate(tm)
> Pro*
> 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:
>>
>>> *This message was transferred with a trial version of CommuniGate(tm)
>>> Pro*
>>> 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
>
>
--
DrMajorBob at bigfoot.com
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