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

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105410] Re: [mg105382] Re: [mg105341] Re: Bug ??????
  • From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
  • Date: Tue, 1 Dec 2009 04:16:18 -0500 (EST)
  • References: <heqf01$1m4$1@smc.vnet.net> <200911291008.FAA16050@smc.vnet.net> <200911301111.GAA13325@smc.vnet.net> <1BCD9E65-ACEB-46FD-9A03-DB8344FE86D7@mimuw.edu.pl> <op.u37k270qtgfoz2@bobbys-imac.local>

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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