Oops! Actually spectacularly bad. I didn't see the positive exponent! Curiously, there appears to be just one bad apple:
> sort(Mod(p(z))) [1] 1.062855e-10 1.062855e-10 1.328999e-10 1.328999e-10 2.579625e-10 [6] 2.579625e-10 3.834721e-10 3.834721e-10 3.875288e-10 3.875288e-10 [11] 5.287459e-10 5.287459e-10 5.306241e-10 5.306241e-10 6.678424e-10 [16] 6.678424e-10 6.876300e-10 6.876300e-10 8.519089e-10 8.519089e-10 [21] 9.345531e-10 9.345531e-10 9.369015e-10 9.369015e-10 9.789510e-10 [26] 9.789510e-10 1.041601e-09 1.041601e-09 1.046996e-09 1.046996e-09 [31] 1.149073e-09 1.149073e-09 1.209875e-09 1.209875e-09 1.232793e-09 [36] 1.232793e-09 1.244167e-09 1.244167e-09 1.388979e-09 1.388979e-09 [41] 1.556354e-09 1.556354e-09 1.596424e-09 1.596424e-09 1.610661e-09 [46] 1.610661e-09 1.722577e-09 1.722577e-09 1.727842e-09 1.727842e-09 [51] 1.728728e-09 1.728728e-09 1.769644e-09 1.769644e-09 1.863983e-09 [56] 1.863983e-09 1.895296e-09 1.895296e-09 1.907509e-09 1.907509e-09 [61] 1.948662e-09 1.948662e-09 2.027021e-09 2.027021e-09 2.061063e-09 [66] 2.061063e-09 2.116735e-09 2.116735e-09 2.185764e-09 2.185764e-09 [71] 2.209158e-09 2.209158e-09 2.398479e-09 2.398479e-09 2.404217e-09 [76] 2.404217e-09 2.503279e-09 2.503279e-09 2.643436e-09 2.643436e-09 [81] 2.654788e-09 2.654788e-09 2.695735e-09 2.695735e-09 2.921933e-09 [86] 2.921933e-09 2.948185e-09 2.948185e-09 2.953596e-09 2.953596e-09 [91] 3.097433e-09 3.097433e-09 3.420593e-09 3.420593e-09 3.735880e-09 [96] 3.735880e-09 4.190042e-09 4.554964e-09 4.554964e-09 1.548112e+15 > Bill Venables CSIRO Laboratories PO Box 120, Cleveland, 4163 AUSTRALIA Office Phone (email preferred): +61 7 3826 7251 Fax (if absolutely necessary): +61 7 3826 7304 Mobile: +61 4 8819 4402 Home Phone: +61 7 3286 7700 mailto:[EMAIL PROTECTED] http://www.cmis.csiro.au/bill.venables/ -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Venables, Bill (CMIS, Cleveland) Sent: Sunday, 25 May 2008 10:58 AM To: [EMAIL PROTECTED]; [EMAIL PROTECTED] Cc: [EMAIL PROTECTED]; [EMAIL PROTECTED]; [EMAIL PROTECTED] Subject: [ExternalEmail] Re: [R] Solving 100th order equation > library(PolynomF) > x <- polynom() > p <- x^100 - 2*x^99 + 10*x^50 + 6*x - 4000 > z <- solve(p) > z [1] -1.0741267+0.0000000i -1.0739999-0.0680356i -1.0739999+0.0680356i -1.0655699-0.1354644i [5] -1.0655699+0.1354644i -1.0568677-0.2030274i -1.0568677+0.2030274i -1.0400346-0.2687815i ... [93] 1.0595174+0.2439885i 1.0746575-0.1721335i 1.0746575+0.1721335i 1.0828132-0.1065591i [97] 1.0828132+0.1065591i 1.0879363-0.0330308i 1.0879363+0.0330308i 2.0000000+0.0000000i > Now to check how good they are: > > range(Mod(p(z))) [1] 1.062855e-10 1.548112e+15 > Not brilliant, but not too bad. Bill Venables CSIRO Laboratories PO Box 120, Cleveland, 4163 AUSTRALIA Office Phone (email preferred): +61 7 3826 7251 Fax (if absolutely necessary): +61 7 3826 7304 Mobile: +61 4 8819 4402 Home Phone: +61 7 3286 7700 mailto:[EMAIL PROTECTED] http://www.cmis.csiro.au/bill.venables/ -----Original Message----- From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] On Behalf Of Gabor Grothendieck Sent: Sunday, 25 May 2008 10:09 AM To: Shubha Vishwanath Karanth Cc: [EMAIL PROTECTED]; Duncan Murdoch; Peter Dalgaard Subject: Re: [R] Solving 100th order equation Actually maybe I was premature. It does not handle the polynomial I tried it on in the example earlier in this thread but it does seem to work with the following very simple polynomials of order 100. At any rate it would not take long to try it on the real problem and see. > Solve(x^100 - 1, x) [1] "Starting Yacas!" expression(list(x == complex_cartesian(cos(pi/50), sin(pi/50)), x == complex_cartesian(cos(pi/25), sin(pi/25)), x == complex_cartesian(cos(3 * pi/50), sin(3 * pi/50)), x == complex_cartesian(cos(2 * pi/25), sin(2 * pi/25)), x == complex_cartesian(cos(pi/10), (root(5, 2) - 1)/4), x == complex_cartesian(cos(3 * pi/25), sin(3 * pi/25)), x == complex_cartesian(cos(7 * pi/50), sin(7 * pi/50)), x == complex_cartesian(cos(4 * pi/25), sin(4 * pi/25)), x == complex_cartesian(cos(9 * pi/50), sin(9 * pi/50)), x == complex_cartesian(cos(pi/5), sin(pi/5)), x == complex_cartesian(cos(11 * pi/50), sin(11 * pi/50)), x == complex_cartesian(cos(6 * pi/25), sin(6 * pi/25)), x == complex_cartesian(cos(13 * pi/50), sin(13 * pi/50)), x == complex_cartesian(cos(7 * pi/25), sin(7 * pi/25)), x == complex_cartesian(cos(3 * pi/10), sin(3 * pi/10)), x == complex_cartesian(cos(8 * pi/25), sin(8 * pi/25)), x == complex_cartesian(cos(17 * pi/50), sin(17 * pi/50)), x == complex_cartesian(cos(9 * pi/25), sin(9 * pi/25)), x == complex_cartesian(cos(19 * pi/50), sin(19 * pi/50)), x == complex_cartesian((root(5, 2) - 1)/4, sin(2 * pi/5)), x == complex_cartesian(cos(21 * pi/50), sin(21 * pi/50)), x == complex_cartesian(cos(11 * pi/25), sin(11 * pi/25)), x == complex_cartesian(cos(23 * pi/50), sin(23 * pi/50)), x == complex_cartesian(cos(12 * pi/25), sin(12 * pi/25)), x == complex_cartesian(0, 1), x == complex_cartesian(-cos(12 * pi/25), sin(12 * pi/25)), x == complex_cartesian(-cos(23 * pi/50), sin(23 * pi/50)), x == complex_cartesian(-cos(11 * pi/25), sin(11 * pi/25)), x == complex_cartesian(-cos(21 * pi/50), sin(21 * pi/50)), x == complex_cartesian(-((root(5, 2) - 1)/4), sin(2 * pi/5)), x == complex_cartesian(-cos(19 * pi/50), sin(19 * pi/50)), x == complex_cartesian(-cos(9 * pi/25), sin(9 * pi/25)), x == complex_cartesian(-cos(17 * pi/50), sin(17 * pi/50)), x == complex_cartesian(-cos(8 * pi/25), sin(8 * pi/25)), x == complex_cartesian(-cos(3 * pi/10), sin(3 * pi/10)), x == complex_cartesian(-cos(7 * pi/25), sin(7 * pi/25)), x == complex_cartesian(-cos(13 * pi/50), sin(13 * pi/50)), x == complex_cartesian(-cos(6 * pi/25), sin(6 * pi/25)), x == complex_cartesian(-cos(11 * pi/50), sin(11 * pi/50)), x == complex_cartesian(-cos(pi/5), sin(pi/5)), x == complex_cartesian(-cos(9 * pi/50), sin(9 * pi/50)), x == complex_cartesian(-cos(4 * pi/25), sin(4 * pi/25)), x == complex_cartesian(-cos(7 * pi/50), sin(7 * pi/50)), x == complex_cartesian(-cos(3 * pi/25), sin(3 * pi/25)), x == complex_cartesian(-cos(pi/10), (root(5, 2) - 1)/4), x == complex_cartesian(-cos(2 * pi/25), sin(2 * pi/25)), x == complex_cartesian(-cos(3 * pi/50), sin(3 * pi/50)), x == complex_cartesian(-cos(pi/25), sin(pi/25)), x == complex_cartesian(-cos(pi/50), sin(pi/50)), x == -1, x == complex_cartesian(-cos(pi/50), -sin(pi/50)), x == complex_cartesian(-cos(pi/25), -sin(pi/25)), x == complex_cartesian(-cos(3 * pi/50), -sin(3 * pi/50)), x == complex_cartesian(-cos(2 * pi/25), -sin(2 * pi/25)), x == complex_cartesian(-cos(pi/10), -((root(5, 2) - 1)/4)), x == complex_cartesian(-cos(3 * pi/25), -sin(3 * pi/25)), x == complex_cartesian(-cos(7 * pi/50), -sin(7 * pi/50)), x == complex_cartesian(-cos(4 * pi/25), -sin(4 * pi/25)), x == complex_cartesian(-cos(9 * pi/50), -sin(9 * pi/50)), x == complex_cartesian(-cos(pi/5), -sin(pi/5)), x == complex_cartesian(-cos(11 * pi/50), -sin(11 * pi/50)), x == complex_cartesian(-cos(6 * pi/25), -sin(6 * pi/25)), x == complex_cartesian(-cos(13 * pi/50), -sin(13 * pi/50)), x == complex_cartesian(-cos(7 * pi/25), -sin(7 * pi/25)), x == complex_cartesian(-cos(3 * pi/10), -sin(3 * pi/10)), x == complex_cartesian(-cos(8 * pi/25), -sin(8 * pi/25)), x == complex_cartesian(-cos(17 * pi/50), -sin(17 * pi/50)), x == complex_cartesian(-cos(9 * pi/25), -sin(9 * pi/25)), x == complex_cartesian(-cos(19 * pi/50), -sin(19 * pi/50)), x == complex_cartesian(-((root(5, 2) - 1)/4), -sin(2 * pi/5)), x == complex_cartesian(-cos(21 * pi/50), -sin(21 * pi/50)), x == complex_cartesian(-cos(11 * pi/25), -sin(11 * pi/25)), x == complex_cartesian(-cos(23 * pi/50), -sin(23 * pi/50)), x == complex_cartesian(-cos(12 * pi/25), -sin(12 * pi/25)), x == complex_cartesian(0, -1), x == complex_cartesian(cos(12 * pi/25), -sin(12 * pi/25)), x == complex_cartesian(cos(23 * pi/50), -sin(23 * pi/50)), x == complex_cartesian(cos(11 * pi/25), -sin(11 * pi/25)), x == complex_cartesian(cos(21 * pi/50), -sin(21 * pi/50)), x == complex_cartesian((root(5, 2) - 1)/4, -sin(2 * pi/5)), x == complex_cartesian(cos(19 * pi/50), -sin(19 * pi/50)), x == complex_cartesian(cos(9 * pi/25), -sin(9 * pi/25)), x == complex_cartesian(cos(17 * pi/50), -sin(17 * pi/50)), x == complex_cartesian(cos(8 * pi/25), -sin(8 * pi/25)), x == complex_cartesian(cos(3 * pi/10), -sin(3 * pi/10)), x == complex_cartesian(cos(7 * pi/25), -sin(7 * pi/25)), x == complex_cartesian(cos(13 * pi/50), -sin(13 * pi/50)), x == complex_cartesian(cos(6 * pi/25), -sin(6 * pi/25)), x == complex_cartesian(cos(11 * pi/50), -sin(11 * pi/50)), x == complex_cartesian(cos(pi/5), -sin(pi/5)), x == complex_cartesian(cos(9 * pi/50), -sin(9 * pi/50)), x == complex_cartesian(cos(4 * pi/25), -sin(4 * pi/25)), x == complex_cartesian(cos(7 * pi/50), -sin(7 * pi/50)), x == complex_cartesian(cos(3 * pi/25), -sin(3 * pi/25)), x == complex_cartesian(cos(pi/10), -((root(5, 2) - 1)/4)), x == complex_cartesian(cos(2 * pi/25), -sin(2 * pi/25)), x == complex_cartesian(cos(3 * pi/50), -sin(3 * pi/50)), x == complex_cartesian(cos(pi/25), -sin(pi/25)), x == complex_cartesian(cos(pi/50), -sin(pi/50)), x == 1)) On Sat, May 24, 2008 at 8:56 AM, Shubha Vishwanath Karanth <[EMAIL PROTECTED]> wrote: > Was also wondering which theoretical method is used to solve this problem? > > Thanks, > Shubha Karanth | Amba Research > Ph +91 80 3980 8031 | Mob +91 94 4886 4510 > Bangalore * Colombo * London * New York * San José * Singapore * > www.ambaresearch.com > > -----Original Message----- > From: Gabor Grothendieck [mailto:[EMAIL PROTECTED] > Sent: Saturday, May 24, 2008 6:13 PM > To: Peter Dalgaard > Cc: Shubha Vishwanath Karanth; [EMAIL PROTECTED]; Duncan Murdoch > Subject: Re: [R] Solving 100th order equation > > On Sat, May 24, 2008 at 8:31 AM, Peter Dalgaard > <[EMAIL PROTECTED]> wrote: >> Shubha Vishwanath Karanth wrote: >>> >>> To apply uniroot I don't even know the interval values... Does numerical >>> methods help me? Or any other method? >>> >>> Thanks and Regards, >>> Shubha >>> >>> -----Original Message----- >>> From: Duncan Murdoch [mailto:[EMAIL PROTECTED] Sent: Saturday, May 24, >>> 2008 5:08 PM >>> To: Shubha Vishwanath Karanth >>> Subject: Re: [R] Solving 100th order equation >>> >>> Shubha Vishwanath Karanth wrote: >>> >>>> >>>> Hi R, >>>> >>>> >>>> I have a 100th order equation for which I need to solve the value for x. >>>> Is there a package to do this? >>>> >>>> >>>> For example my equation is: >>>> >>>> >>>> (x^100 )- (2*x^99) +(10*x^50)+.............. +(6*x ) = 4000 >>>> >>>> >>>> I have only one unknown value and that is x. How do I solve for this? >>>> >>>> >>> >>> uniroot() will find one root. If you want all of them, I don't know what >>> is available. >>> >>> Duncan Murdoch >>> >> >> polyroot() is built for this, but it stops at 48th degree polynomials, at >> least as currently implemented. Not sure that it (or anything else) would be >> stable beyond that limit. YACAS perhaps? >> > > Unfortunately yacas does not seem to be able to handle it: > >> library(Ryacas) >> x <- Sym("x") >> Solve((x^100 )- (2*x^99) +(10*x^50)+(6*x ) - 4000 == 0, x) > [1] "Starting Yacas!" > expression(list()) > > Simpler one works ok: > >> Solve(x^2 - 1, x) > expression(list(x == 1, x == -1)) > This e-mail may contain confidential and/or privileged...{{dropped:12}} ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code. ______________________________________________ R-help@r-project.org mailing list https://stat.ethz.ch/mailman/listinfo/r-help PLEASE do read the posting guide http://www.R-project.org/posting-guide.html and provide commented, minimal, self-contained, reproducible code.
