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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
## @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