Bfloat allroots

Hi Ray,


Thx for polyroots . (:-))

I have been used polyroots to :
-find complex roots of polynomials :
  http://fraktal.republika.pl/doc/polyroots.txt
  http://fraktal.republika.pl/doc/polyroots_new.txt
http://commons.wikimedia.org/wiki/File:ComponentNewton.jpg
( Can I improve it ?)
  It was better then allroots ( 1 period) :
  http://fraktal.republika.pl/mset_centers.html

( you can compare my ( may be errors) results with other programs :
MPSolve : http://fraktal.republika.pl/doc/m_c_all_g_new.txt
WebSolver : http://fraktal.republika.pl/doc/websolve_solutions.txt
Octave : http://fraktal.republika.pl/doc/octave.txt
real component centers of Mandelbrot Set for period less than 16 by Jay 
R. Hill :
http://fraktal.republika.pl/doc/REALONLY.TXT




HTH


Adam










Raymond Toy pisze:
> Some time ago, I wrote jtroot3.mac (share/numeric) to compute roots of
> polynomials using Jenkins-Traub algorithm.  It mostly works, but some
> simple polynomials fail (see https://sourceforge.net/tracker2/?func=detail&aid=2230778&group_id=4933&atid=104933).
> 
> What I should have done is taken the existing allroots implementation
> and converted it to use bfloats.  Well, here it is:
> http://common-lisp.net/~rtoy/bfcpoly.lisp.
> 
> There are probably bugs, but the few tests I tried seem to work, and
> the above bug is gone.
> 
> While doing this, I also found the undocumented polyfactor variable.
> When polyfactor is false, bfallroots and allroots return a list of the
> roots.  When polyfactor is true, bfallroots and allroots return the
> result as a factored polynomial of the form c*(x-r1)*(x-r2)...
> 
> Perhaps this can be placed in cpoly.lisp or maybe as a contrib in
> share/numeric.
> 
> Also, I should probably also convert rpoly-sl to support bfloats, and
> then allroots and bfallroots will be functionally identical.
> 
> Hope this is useful to someone,
> 
> Ray