Re: Re: Re: Bug ??????
- To: mathgroup at smc.vnet.net
- Subject: [mg105408] Re: [mg105382] Re: [mg105341] Re: Bug ??????
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Tue, 1 Dec 2009 04:15:52 -0500 (EST)
- References: <heqf01$1m4$1@smc.vnet.net> <200911291008.FAA16050@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
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]= >>> 2.267459811963931497406941878036067357307998685435567904057927238778317779198056926405182471544211907*10^-44 >>> >>> Sam >>> >>> >> >> >> -- >> DrMajorBob at yahoo.com >> > -- DrMajorBob at yahoo.com