/usr/share/octave/packages/communications-1.1.1/@galois/roots.m is in octave-communications-common 1.1.1-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
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 74 75 | ## 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
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