Re: Bug ??????
- To: mathgroup at smc.vnet.net
- Subject: [mg105352] Re: Bug ??????
- From: sashap <pavlyk at gmail.com>
- Date: Sun, 29 Nov 2009 05:10:06 -0500 (EST)
- References: <heqf01$1m4$1@smc.vnet.net>
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? *) In[13]:= z = RootReduce[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]]; In[14]:= RootReduce[F[z]] Out[14]= 18339659776 You can also verify the result numerically using extended precision: In[16]:= N[F[Sqrt[Sqrt[2] + 3^(1/3)] + 1/Sqrt[3^(1/3) + 5^(1/5)]], 50] Out[16]= 1.8339659776`50.*^10 Machine precision numerical evaluation gives garbage due to catastrophic cancellation, i.e. subtraction of two close large numbers canceling all significant digits. Hope this helps, Oleksandr Pavlyk Wolfram Research