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Re: Bug ??????

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105563] Re: Bug ??????
  • From: anguzman at ing.uchile.cl
  • Date: Wed, 9 Dec 2009 05:43:01 -0500 (EST)
  • References: <heqf01$1m4$1@smc.vnet.net>

Hi All:
I checked this "bug" and the thing is wrong from the beginning, the last lin=
e
of the polinomial is
...403671859200*x^118  + 18339659776  + 18339659776 *x^120
the middle term is a constant and is exactly the residual found..
  1.83396597760000000000000000000000000000000000000000000000000000000000\
  0000000000000000000000000000000*10^10

The root proposed is a root of the polinomial without this term.
Using Expand and then  Simplify in Mathematica 6.0.3 gives  a nice 0

However, I couldn't get this integer applying Expand and Simplify to
the original expression.


Atte. Andres Guzman




Andrzej Kozlowski <akoz at mimuw.edu.pl> ha escrito:

> Sorry, my misunderstanding. I thought you meant that it still might  
> be a root.
> ( In fact to prove that it is not a root one just a few digits would 
>  be enough (unless they turn out to be zero) since N guarantees the  
> specified number of digits to be correct.)
>
> Andrzej
>
> On 30 Nov 2009, at 22:00, DrMajorBob wrote:
>
>> 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]=
>>>>> =
> 2.267459811963931497406941878036067357307998685435567904057927238778317779=
=
> 198056926405182471544211907*10^-44
>>>>>
>>>>> Sam
>>>>>
>>>>>
>>>>
>>>>
>>>> --
>>>> DrMajorBob at yahoo.com
>>>>
>>>
>>
>>
>> --
>> DrMajorBob at yahoo.com
>
>
>



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