maint: Use Octave coding conventions for cuddling parentheses in scripts directory * lin2mu.m, loadaudio.m, wavread.m, accumarray.m, bicubic.m, celldisp.m, colon.m, cplxpair.m, dblquad.m, divergence.m, genvarname.m, gradient.m, int2str.m, interp1.m, interp1q.m, interp2.m, interpn.m, loadobj.m, nthargout.m, __isequal__.m, __splinen__.m, quadgk.m, quadl.m, quadv.m, rat.m, rot90.m, rotdim.m, saveobj.m, subsindex.m, triplequad.m, delaunay3.m, griddata.m, inpolygon.m, tsearchn.m, voronoi.m, get_first_help_sentence.m, which.m, gray2ind.m, pink.m, dlmwrite.m, strread.m, textread.m, textscan.m, housh.m, ishermitian.m, issymmetric.m, krylov.m, logm.m, null.m, rref.m, compare_versions.m, copyfile.m, dump_prefs.m, edit.m, fileparts.m, getappdata.m, isappdata.m, movefile.m, orderfields.m, parseparams.m, __xzip__.m, rmappdata.m, setappdata.m, swapbytes.m, unpack.m, ver.m, fminbnd.m, fminunc.m, fsolve.m, glpk.m, lsqnonneg.m, qp.m, sqp.m, configure_make.m, copy_files.m, describe.m, get_description.m, get_forge_pkg.m, install.m, installed_packages.m, is_architecture_dependent.m, load_package_dirs.m, print_package_description.m, rebuild.m, repackage.m, save_order.m, shell.m, allchild.m, ancestor.m, area.m, axes.m, axis.m, clabel.m, close.m, colorbar.m, comet.m, comet3.m, contour.m, cylinder.m, ezmesh.m, ezsurf.m, findobj.m, fplot.m, hist.m, isocolors.m, isonormals.m, isosurface.m, isprop.m, legend.m, mesh.m, meshz.m, pareto.m, pcolor.m, peaks.m, plot3.m, plotmatrix.m, plotyy.m, polar.m, print.m, __add_datasource__.m, __add_default_menu__.m, __axes_limits__.m, __bar__.m, __clabel__.m, __contour__.m, __errcomm__.m, __errplot__.m, __ezplot__.m, __file_filter__.m, __fltk_print__.m, __ghostscript__.m, __gnuplot_print__.m, __go_draw_axes__.m, __go_draw_figure__.m, __interp_cube__.m, __marching_cube__.m, __patch__.m, __pie__.m, __plt__.m, __print_parse_opts__.m, __quiver__.m, __scatter__.m, __stem__.m, __tight_eps_bbox__.m, __uigetdir_fltk__.m, __uigetfile_fltk__.m, __uiputfile_fltk__.m, quiver.m, quiver3.m, rectangle.m, refreshdata.m, ribbon.m, scatter.m, semilogy.m, shading.m, slice.m, subplot.m, surface.m, surfl.m, surfnorm.m, text.m, uigetfile.m, uiputfile.m, whitebg.m, deconv.m, mkpp.m, pchip.m, polyaffine.m, polyder.m, polygcd.m, polyout.m, polyval.m, ppint.m, ppjumps.m, ppval.m, residue.m, roots.m, spline.m, splinefit.m, addpref.m, getpref.m, setpref.m, ismember.m, setxor.m, arch_fit.m, arch_rnd.m, arch_test.m, autoreg_matrix.m, diffpara.m, fftconv.m, filter2.m, hanning.m, hurst.m, periodogram.m, triangle_sw.m, sinc.m, spectral_xdf.m, spencer.m, stft.m, synthesis.m, unwrap.m, yulewalker.m, bicgstab.m, gmres.m, pcg.m, pcr.m, __sprand_impl__.m, speye.m, spfun.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, bessel.m, factor.m, legendre.m, perms.m, primes.m, magic.m, toeplitz.m, corr.m, cov.m, mean.m, median.m, mode.m, qqplot.m, quantile.m, ranks.m, zscore.m, logistic_regression_likelihood.m, bartlett_test.m, chisquare_test_homogeneity.m, chisquare_test_independence.m, kolmogorov_smirnov_test.m, run_test.m, u_test.m, wilcoxon_test.m, z_test.m, z_test_2.m, bin2dec.m, dec2base.m, mat2str.m, strcat.m, strchr.m, strjust.m, strtok.m, substr.m, untabify.m, assert.m, demo.m, example.m, fail.m, speed.m, test.m, now.m: Use Octave coding conventions for cuddling parentheses in scripts directory.

## Copyright (C) 2000-2012 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 3 of the License, 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, see
## <http://www.gnu.org/licenses/>.

## -*- 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}} and every element of @var{p} is a prime
## number.  If @code{@var{q} == 1}, return 1.
##
## With two output arguments, return the unique primes @var{p} and
## their multiplicities.  That is, @code{prod (@var{p} .^ @var{n}) ==
## @var{q}}.
## @seealso{gcd, lcm}
## @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, n] = factor (q)

  if (nargin < 1)
    print_usage ();
  endif

  if (! isscalar (q) || q != fix (q))
    error ("factor: Q must be a scalar integer");
  endif

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

  x = [];
  ## There is at most one prime greater than sqrt(q), and if it exists,
  ## it has multiplicity 1, so no need to consider any factors greater
  ## than sqrt(q) directly. [If there were two factors p1, p2 > sqrt(q),
  ## then q >= p1*p2 > sqrt(q)*sqrt(q) == q. Contradiction.]
  p = primes (sqrt (q));
  while (q > 1)
    ## Find prime factors in remaining q.
    p = p (rem (q, p) == 0);
    if (isempty (p))
      ## Can't be reduced further, so q must itself be a prime.
      p = q;
    endif
    x = [x, p];
    ## Reduce q.
    q = q / prod (p);
  endwhile
  x = sort (x);

  ## Determine muliplicity.
  if (nargout > 1)
    idx = find ([0, x] != [x, 0]);
    x = x(idx(1:length (idx)-1));
    n = diff (idx);
  endif

endfunction


%!assert (factor (1), 1)
%!test
%! 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]));
%! endfor