I thought it was the first example in p. since I never realized there was a p.. I thought I was getting roots of a polynomial which I have used.
Sorry. Linda -----Original Message----- From: [email protected] [mailto:[email protected]] On Behalf Of Roger Hui Sent: Thursday, January 7, 2016 9:27 AM To: Programming forum Subject: Re: [Jprogramming] the p. equation solver I don't understand your question. p. (one dot) is different from p.. (two dots), and all four examples in your msgs seem correct. On Thu, Jan 7, 2016 at 2:58 AM, Linda A Alvord <[email protected]> wrote: > Roger, > > If I type in fresh jqt: > > p. 1 2 3 4 5 > > ┌─┬─────────────────────────────────────────────────────────────────── > ────────┐ > │5│0.137832j0.678154 0.137832j_0.678154 _0.537832j0.358285 > _0.537832j_0.358285│ > > └─┴───────────────────────────────────────────────────────────────────────────┘ > p.. 1 2 3 4 5 > 2 6 12 20 > > However I get the same answer when I copied the example in the > vocabulary in the second example. > > What explains this? > > Linda > > -----Original Message----- > From: [email protected] [mailto: > [email protected]] On Behalf Of Roger Hui > Sent: Thursday, January 7, 2016 2:20 AM > To: Programming forum > Subject: Re: [Jprogramming] the p. equation solver > > p. uses Laguerre's Method with polishing on the original polynomial > using Newton iteration. It can no doubt be simplified and/or improved. > > A couple of examples of using p. : > > c=: p. <1+i.20 > $c > 21 > 3 7$c > 2432902008176640000 _8752948036761600000 13803759753640704000 > _12870931245150988800 8037811822645051776 _3599979517947607200 > 1206647803780373360 > _311333643161390640 63030812099294896 _10142299865511450 > 1307535010540395 _135585182899530 11310276995381 > _756111184500 > 40171771630 _1672280820 53327946 > _1256850 20615 _210 1 > > c are the coefficient's of Wilkinson's polynomial < > https://en.wikipedia.org/wiki/Wilkinson%27s_polynomial>, whose roots > are > > p. c > ┌─┬──────────────────────────────────────────────────┐ > │1│20 19 18 17 16 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1│ > └─┴──────────────────────────────────────────────────┘ > > > > On Wed, Jan 6, 2016 at 10:53 PM, 'Bo Jacoby' via Programming < > [email protected]> wrote: > > > Dear experts. > > The equation solver (p.) is marvelous! However I do not know how it > > is implemented. > > Computing the complex roots of algebraic equations should be > > considered basic. If you can do that, then you need not to learn > > about division or square roots. > > I made this elementary equation solver in J. (Durand-Kerner method). > > > > poly =.+/@([*]^~/~i.@#@[) > > > > step=.]-poly*[:*/-/~@]^<:@=/~@i.@<:@#@[ > > > > iter =.](step^:_)_0.4j0.9^i.@<:@# norm =.[:(% > {:)]}.~[:-[:+/[:*/\0=|. > > solv =.iter@norm > > A polynomial is represented by an array of coefficients, the > > constant term first. > > poly computes values of a polynomial. > > 0 40 0 _10 0 0 poly i:4 > > 480 150 0 _30 0 30 0 _150 _480 > > norm normalizes a polynomial such that the leading coefficient is > > one, without changing the roots. > > norm 0 40 0 _10 0 0 > > 0 _4 0 1 > > step improves a set of approximate roots to a normalized polynomial. > > 0 _4 0 1 step _0.4j0.9^i.3 > > 1.98849j0.159402 _0.860465j_0.735105 _1.12803j0.575703 iter makes a > > sufficient number of steps. > > iter 0 _4 0 1 > > 2 0 _2 > > solv solves even non-normalized polynomials > > solv 0 40 0 _10 0 0 > > 2 0 _2 > > My questions: > > 1. Is this how (p.) is implemented? > > 2. Can it be simplified or improved? > > Thanks! Bo. > > -------------------------------------------------------------------- > > -- For information about J forums see > > http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
