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Re: Re: Bug ??????

  • To: mathgroup at smc.vnet.net
  • Subject: [mg105382] Re: [mg105341] Re: Bug ??????
  • From: DrMajorBob <btreat1 at austin.rr.com>
  • Date: Mon, 30 Nov 2009 06:11:55 -0500 (EST)
  • References: <heqf01$1m4$1@smc.vnet.net> <200911291008.FAA16050@smc.vnet.net>
  • Reply-to: drmajorbob at yahoo.com

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


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