Re: Re: Re: Bug ??????
- To: mathgroup at smc.vnet.net
- Subject: [mg105398] Re: [mg105382] Re: [mg105341] Re: Bug ??????
- From: Andrzej Kozlowski <akoz at mimuw.edu.pl>
- Date: Tue, 1 Dec 2009 04:13:58 -0500 (EST)
- References: <heqf01$1m4$1@smc.vnet.net> <200911291008.FAA16050@smc.vnet.net> <200911301111.GAA13325@smc.vnet.net>
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 >