## Copyright (C) 2000 Paul Kienzle
##
## 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, write to the Free Software
## Foundation, Inc., 59 Temple Place, Suite 330, Boston, MA  02111-1307  USA

## -*- texinfo -*-
## @deftypefn {Function File} {} factor (@var{q})
## Return prime factorization of @var{q}.  If n==1, returns 1.
## @deftypefnx {Function File} {[@var{p},@var{n}] = } factor (@var{q})
## Return the unique primes @var{p} and their multiplicity.
## @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)
    usage("[p, n] = factor(q)");
  endif
  if (n != fix(n))
    error("factor only works for integers");
  endif

  ## special case of no primes less than sqrt(n)
  if (n < 4)
    x = n;
    m = 1;
    return;
  endif 

  x = NaN; # silliness to avoid empty matrix concatenation warnings
  ## 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(2:length(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