## [b37be7]: / inst / @galois / roots.m  Maximize  Restore  History

 ``` 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73``` ```## Copyright (C) 2002 David Bateman ## ## This program is free software; you can redistribute it and/or modify it under ## the terms of the GNU General Public License as published by the Free Software ## Foundation; either version 3 of the License, or (at your option) any later ## version. ## ## This program is distributed in the hope that it will be useful, but WITHOUT ## ANY WARRANTY; without even the implied warranty of MERCHANTABILITY or ## FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License for more ## details. ## ## You should have received a copy of the GNU General Public License along with ## this program; if not, see . ## -*- texinfo -*- ## @deftypefn {Function File} {} roots (@var{v}) ## ## For a vector @var{v} with @math{N} components, return ## the roots of the polynomial over a Galois Field ## @tex ## \$\$ ## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N. ## \$\$ ## @end tex ## @ifnottex ## ## @example ## v(1) * z^(N-1) + ... + v(N-1) * z + v(N). ## @end example ## @end ifnottex ## ## The number of roots returned and their value will be determined ## by the order and primitive polynomial of the Galois Field ## @end deftypefn function r = roots (v) if (nargin != 1) print_usage (); endif if (!isgalois (v)) error ("roots: argument must be a galois variable"); endif if (min (size (v)) > 1 || nargin != 1) print_usage (); endif v = reshape (v, 1, length (v)); m = v.m; prim_poly = v.prim_poly; n = 2^m - 1; poly = v; nr = 0; t = 0; r = []; while ((t <= n) && (length (poly) > 1)) [npoly, nrem] = deconv (poly, gf ([1, t], m, prim_poly)); if (any (nrem)) t = t + 1; else nr = nr + 1; r(nr) = t; poly = npoly; endif endwhile r = gf (r, m, prim_poly); endfunction ```