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view main/comm/inst/@galois/roots.m @ 9666:67d4cfc5eeb3 octave-forge
comm: update license to GPLv3+
author | carandraug |
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date | Tue, 13 Mar 2012 04:31:21 +0000 |
parents | 90a46621a91d |
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## 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 <http://www.gnu.org/licenses/>. ## -*- 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 ## @iftex ## @tex ## $$ ## v_1 z^{N-1} + \cdots + v_{N-1} z + v_N. ## $$ ## @end tex ## @end iftex ## @ifinfo ## ## @example ## v(1) * z^(N-1) + ... + v(N-1) * z + v(N). ## @end example ## @end ifinfo ## ## The number of roots returned and their value will be determined ## by the order and primitive polynomial of the Galios Field ## @end deftypefn function r = roots (v) if (nargin != 1) error("usage: r = roots(v)"); endif if (!isgalois(v)) error("roots: argument must be a galois variable"); endif if (min (size (v)) > 1 || nargin != 1) usage ("roots (v), where v is a galois vector"); 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 end r = gf(r,m,prim_poly); endfunction