--- a
+++ b/inst/@gf/roots.m
@@ -0,0 +1,80 @@
+## Copyright (C) 2011 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 2 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 = v._n;
+  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
+
+%!test
+%! poly1 = gf([2,4,5,1],3);
+%! roots1 = roots(poly1);
+%! assert(polyval(poly1, roots1), gf([0,0,0],3))