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Re: Re: Re: Bug ??????

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105408] Re: [mg105382] Re: [mg105341] Re: Bug ??????
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Tue, 1 Dec 2009 04:15:52 -0500 (EST)
  • References: <heqf01$1m4$1@smc.vnet.net> <200911291008.FAA16050@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

I only mean that it's hard to find (without the Roots routine) x values  
for which Abs@F@x is smaller. With terms like 18339659776 *x^120 included,  
it's not hard to get values larger than 2*10^10. The function is extremely  
"noisy", one might say.

I do NOT mean that the OP's "candidate root" is a root. N[F@expr,100]  
proved that it isn't.

Bobby

On Mon, 30 Nov 2009 06:34:30 -0600, Andrzej Kozlowski <akoz at mimuw.edu.pl>  
wrote:

> What exactly do you mean? Here Mathematica has proved (I mean really  
> *proved*) that the candidate root is not a root at all. That is, unless  
> there is a serious bug (and I mean bug) in Mathematica's significance  
> arithmetic. If that were so, it would be a very serious bug indeed,  
> perhaps the worst that has ever been found.
>
> Andrzej Kozlowski
>
> On 30 Nov 2009, at 20:11, DrMajorBob wrote:
>
>> The candidate root yields a high value:
>>
>> N[F@expr, 100]
>>
>> 1.83396597760000000000000000000000000000000000000000000000000000000000\
>> 0000000000000000000000000000000*10^10
>>
>> But it's not particularly high, OTOH, considering the powers and
>> coefficients involved.
>>
>> Bobby
>>
>> On Sun, 29 Nov 2009 04:08:02 -0600, Emu <samuel.thomas.blake at gmail.com>
>> wrote:
>>
>>> On Nov 28, 12:12 am, ynb <wkfkh... at yahoo.co.jp> wrote:
>>>> F[x_]:=34880228747203264624081936 -
>>>> 464212176939061350196344960*x^2 +
>>>> 4201844995162976506469882880*x^4 -
>>>> 36736184611200699915890392480*x^6 +
>>>> 245136733977616412716801297320*x^8 -
>>>> 1144143594851571569661248433072*x^10 +
>>>> 3682862525053500791559515638600*x^12 -
>>>> 8693355704402316431096075720520*x^14 +
>>>> 16394872503384952006491292949865*x^16 -
>>>> 26387316917169915527289585290460*x^18 +
>>>> 37452280566060594746358503070858*x^20 -
>>>> 47740404486181766316209780642820*x^22 +
>>>> 55423947476122401752437921213065*x^24 -
>>>> 58870208625780045323379674540820*x^26 +
>>>> 58030587837504412314635631719520*x^28 -
>>>> 54472073947308977321830018366176*x^30 +
>>>> 49239457796351067392552601696240*x^32 -
>>>> 43012853616400258712689244528460*x^34 +
>>>> 36323948931672906173046609029970*x^36 -
>>>> 29377569489403484765569859203920*x^38 +
>>>> 22788548915181561726713932258680*x^40 -
>>>> 16857194550514400031853658104200*x^42 +
>>>> 11584615647879044636617246631070*x^44 -
>>>> 7411292928519764848064641481820*x^46 +
>>>> 4455112744096674126517658718330*x^48 -
>>>> 2438996599504313974964504461440*x^50 +
>>>> 1194689292448727425260627641460*x^52 -
>>>> 524949326441431396920558140380*x^54 +
>>>> 201021537824162724562860099525*x^56 -
>>>> 61015761298172117757282456180*x^58 +
>>>> 8304189679978507974953617206*x^60 +
>>>> 2576525048464159376125949700*x^62 -
>>>> 2090208393662742383940297195*x^64 +
>>>> 1986814425386740056472178280*x^66 -
>>>> 689825144661940289046969960*x^68 -
>>>> 74165160041784503310561360*x^70 -
>>>> 43639409581797171854387880*x^72 -
>>>> 306779359014073038922080*x^74 +
>>>> 29021239224919123514667120*x^76 +
>>>> 3148715202822489687194520*x^78 -
>>>> 1180110005143725763548459*x^80 -
>>>> 1198749024197941338242580*x^82 -
>>>> 491140297003511546045670*x^84 +
>>>> 69048887622760819121580*x^86 +
>>>> 69823737459557420754765*x^88 +
>>>> 14776899216873553079620*x^90 -
>>>> 1463855286795400794960*x^92 -
>>>> 2352108554547064743120*x^94 -
>>>> 381175702618028601675*x^96 +
>>>> 126522213276402173400*x^98 +
>>>> 35845283140073787252*x^100 -
>>>> 2394735843271729380*x^102 -
>>>> 1421523086424723225*x^104 -
>>>> 37328586803289300*x^106 +
>>>> 29410426690606450*x^108 +
>>>> 2647220666999700*x^110 -
>>>> 300290705882655*x^112 - 51254703758400*
>>>> x^114 + 500254901760*x^116 +
>>>> 403671859200*x^118  + 18339659776  + 18339659776 *x^120
>>>>
>>>> (*  Bug ?; F[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]]
>>>> //N
>>>> =3.828176627860558*^38<---Bug ?  *)
>>>>
>>>> (* =0? *)
>>>
>>> It appears that the expression Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^
>>> (1/3) + 5^(1/5)] is very close to one of the roots of F[x], but it is
>>> not a zero of F[x].
>>>
>>>
>>> In[117]:= Select[Solve[F[x] == 0, x], (x /. N[#]) \[Element] Reals &]
>>> [[-1, 1, -1]]; (* Returns a large Root object. *)
>>>
>>> In[118]:= N[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)] - %,
>>> 100]
>>> Out[118]=
>>> 2.267459811963931497406941878036067357307998685435567904057927238778317779198056926405182471544211907*10^-44
>>>
>>> Sam
>>>
>>>
>>
>>
>> --
>> DrMajorBob at yahoo.com
>>
>


-- 
DrMajorBob at yahoo.com


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