--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/scripts/specfun/factor.m	Mon May 22 06:25:14 2006 +0000
@@ -0,0 +1,94 @@
+## Copyright (C) 2000 Paul Kienzle
+##
+## This file is part of Octave.
+##
+## Octave 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, or (at your option)
+## any later version.
+##
+## Octave 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 Octave; see the file COPYING.  If not, write to the Free
+## Software Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA
+## 02110-1301, USA.
+
+## -*- texinfo -*-
+## @deftypefn {Function File} {@var{p} =} factor (@var{q})
+## @deftypefnx {Function File} {[@var{p}, @var{n}] =} factor (@var{q})
+##
+## Return prime factorization of @var{q}. That is @code{prod (@var{p})
+## == @var{q}}. If @code{@var{q} == 1}, returns 1. 
+##
+## With two output arguments, returns the uniques primes @var{p} and
+## their mulyiplicities. That is @code{prod (@var{p} .^ @var{n}) ==
+## @var{q}).
+## 
+## @end deftypefn
+
+## Author: Paul Kienzle
+
+## 2002-01-28 Paul Kienzle
+## * remove recursion; only check existing primes for multiplicity > 1
+## * return multiplicity as suggested by Dirk Laurie
+## * add error handling
+
+function [x, m] = factor (n)
+
+  if (nargin < 1)
+    print_usage ();
+  endif
+
+  if (! isscalar (n) || n != fix (n))
+    error ("factor: n must be a scalar integer");
+  endif
+
+  ## special case of no primes less than sqrt(n)
+  if (n < 4)
+    x = n;
+    m = 1;
+    return;
+  endif 
+
+  x = [];
+  ## There is at most one prime greater than sqrt(n), and if it exists,
+  ## it has multiplicity 1, so no need to consider any factors greater
+  ## than sqrt(n) directly. [If there were two factors p1, p2 > sqrt(n),
+  ## then n >= p1*p2 > sqrt(n)*sqrt(n) == n. Contradiction.]
+  p = primes (sqrt (n));
+  while (n > 1)
+    ## find prime factors in remaining n
+    q = n ./ p;
+    p = p (q == fix (q));
+    if (isempty (p))
+      p = n;  # can't be reduced further, so n must itself be a prime.
+    endif
+    x = [x, p];
+    ## reduce n
+    n = n / prod (p);
+  endwhile
+  x = sort (x);
+
+  ## determine muliplicity
+  if (nargout > 1)
+    idx = find ([0, x] != [x, 0]);
+    x = x(idx(1:length(idx)-1));
+    m = diff (idx);
+  endif
+
+endfunction
+
+## test:
+##   assert(factor(1),1);
+##   for i=2:20
+##      p = factor(i);
+##      assert(prod(p),i);
+##      assert(all(isprime(p)));
+##      [p,n] = factor(i);
+##      assert(prod(p.^n),i);
+##      assert(all([0,p]!=[p,0]));
+##   end