Re: Bug ??????
- To: mathgroup at smc.vnet.net
- Subject: [mg105563] Re: Bug ??????
- From: anguzman at ing.uchile.cl
- Date: Wed, 9 Dec 2009 05:43:01 -0500 (EST)
- References: <heqf01$1m4$1@smc.vnet.net>
Hi All: I checked this "bug" and the thing is wrong from the beginning, the last lin= e of the polinomial is ...403671859200*x^118 + 18339659776 + 18339659776 *x^120 the middle term is a constant and is exactly the residual found.. 1.83396597760000000000000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000*10^10 The root proposed is a root of the polinomial without this term. Using Expand and then Simplify in Mathematica 6.0.3 gives a nice 0 However, I couldn't get this integer applying Expand and Simplify to the original expression. Atte. Andres Guzman Andrzej Kozlowski <akoz at mimuw.edu.pl> ha escrito: > Sorry, my misunderstanding. I thought you meant that it still might > be a root. > ( In fact to prove that it is not a root one just a few digits would > be enough (unless they turn out to be zero) since N guarantees the > specified number of digits to be correct.) > > Andrzej > > On 30 Nov 2009, at 22:00, DrMajorBob wrote: > >> 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]= >>>>> = > 2.267459811963931497406941878036067357307998685435567904057927238778317779= = > 198056926405182471544211907*10^-44 >>>>> >>>>> Sam >>>>> >>>>> >>>> >>>> >>>> -- >>>> DrMajorBob at yahoo.com >>>> >>> >> >> >> -- >> DrMajorBob at yahoo.com > > > ---------------------------------------------------------------- This message was sent using IMP, the Internet Messaging Program.
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- From: David Szekely <D.Szekely@victorchang.edu.au>
- NDSolve: Affecting dependent variable during solution?