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
- References:
- Re: Bug ??????
- From: Emu <samuel.thomas.blake@gmail.com>
- Re: Bug ??????