Eliminate unneeded verification of nargin, nargout in m-files. * FIRfilter.m, FIRfilter_aggregation.m, get.m, polynomial.m, polynomial_superiorto.m, polynomial2.m, makeUniqueStrings.m, base64decode.m, base64encode.m, cd.m, lin2mu.m, record.m, sound.m, soundsc.m, accumarray.m, accumdim.m, bitcmp.m, bitset.m, cart2pol.m, celldisp.m, circshift.m, cplxpair.m, cumtrapz.m, flip.m, idivide.m, interpft.m, logspace.m, pol2cart.m, polyarea.m, postpad.m, prepad.m, rat.m, rot90.m, rotdim.m, shift.m, shiftdim.m, sortrows.m, trapz.m, dsearch.m, dsearchn.m, getappdata.m, getpixelposition.m, guidata.m, guihandles.m, isappdata.m, listfonts.m, uigetdir.m, waitforbuttonpress.m, __makeinfo__.m, doc.m, get_first_help_sentence.m, autumn.m, bone.m, brighten.m, cmpermute.m, cmunique.m, colorcube.m, contrast.m, cool.m, copper.m, cubehelix.m, flag.m, gray.m, gray2ind.m, hot.m, hsv.m, im2double.m, im2frame.m, imformats.m, jet.m, lines.m, ocean.m, pink.m, prism.m, rainbow.m, rgbplot.m, spinmap.m, spring.m, summer.m, viridis.m, white.m, winter.m, beep.m, importdata.m, is_valid_file_id.m, javachk.m, javaclasspath.m, findstr.m, genvarname.m, strmatch.m, bandwidth.m, commutation_matrix.m, cond.m, cross.m, isdefinite.m, ishermitian.m, issymmetric.m, krylov.m, linsolve.m, logm.m, lscov.m, null.m, ordeig.m, orth.m, rank.m, rref.m, vecnorm.m, bunzip2.m, citation.m, computer.m, copyfile.m, dir.m, dos.m, fileattrib.m, gunzip.m, inputParser.m, inputname.m, ismac.m, ispc.m, isunix.m, license.m, list_primes.m, methods.m, mkdir.m, movefile.m, nargchk.m, news.m, orderfields.m, recycle.m, tar.m, unix.m, unpack.m, untar.m, unzip.m, ver.m, version.m, what.m, zip.m, decic.m, fminbnd.m, fminunc.m, fsolve.m, fzero.m, glpk.m, humps.m, lsqnonneg.m, optimget.m, pqpnonneg.m, sqp.m, pathdef.m, camlookat.m, hidden.m, specular.m, plotmatrix.m, smooth3.m, sombrero.m, stemleaf.m, __gnuplot_drawnow__.m, __opengl_info__.m, ancestor.m, cla.m, close.m, closereq.m, copyobj.m, gca.m, gcf.m, ginput.m, graphics_toolkit.m, groot.m, hgload.m, hgsave.m, isgraphics.m, ishold.m, linkaxes.m, meshgrid.m, newplot.m, refresh.m, refreshdata.m, rotate.m, saveas.m, struct2hdl.m, conv.m, mkpp.m, mpoles.m, padecoef.m, pchip.m, polyder.m, polyfit.m, polygcd.m, polyint.m, polyout.m, polyval.m, ppder.m, ppint.m, getpref.m, ispref.m, rmpref.m, profexport.m, profshow.m, powerset.m, arch_fit.m, arma_rnd.m, blackman.m, detrend.m, diffpara.m, fftconv.m, fftfilt.m, filter2.m, freqz.m, freqz_plot.m, hamming.m, hanning.m, sinetone.m, sinewave.m, spectral_adf.m, spectral_xdf.m, stft.m, unwrap.m, gplot.m, ichol.m, ilu.m, spdiags.m, sprand.m, sprandn.m, spstats.m, svds.m, treelayout.m, treeplot.m, betainc.m, betaincinv.m, ellipke.m, gammainc.m, gammaincinv.m, legendre.m, pow2.m, hankel.m, pascal.m, rosser.m, toeplitz.m, bounds.m, corr.m, cov.m, histc.m, kendall.m, kurtosis.m, mad.m, mode.m, moment.m, prctile.m, quantile.m, range.m, ranks.m, run_count.m, skewness.m, spearman.m, std.m, var.m, zscore.m, dec2base.m, dec2bin.m, dec2hex.m, index.m, mat2str.m, native2unicode.m, ostrsplit.m, strjoin.m, strjust.m, strtok.m, substr.m, unicode2native.m, untabify.m, __debug_octave__.m, demo.m, example.m, fail.m, oruntests.m, dump_demos.m, speed.m, test.m, date.m, datenum.m, datestr.m, datevec.m, is_leap_year.m, now.m, weekday.m: Eliminate unneeded verification of nargin, nargout in m-files now that the interpreter checks these values.

########################################################################
##
## Copyright (C) 2000-2020 The Octave Project Developers
##
## See the file COPYRIGHT.md in the top-level directory of this
## distribution or <https://octave.org/copyright/>.
##
## 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
## <https://www.gnu.org/licenses/>.
##
########################################################################

## -*- texinfo -*-
## @deftypefn  {} {@var{q} =} polygcd (@var{b}, @var{a})
## @deftypefnx {} {@var{q} =} polygcd (@var{b}, @var{a}, @var{tol})
##
## Find the greatest common divisor of two polynomials.
##
## This is equivalent to the polynomial found by multiplying together all the
## common roots.  Together with deconv, you can reduce a ratio of two
## polynomials.
##
## The tolerance @var{tol} defaults to @code{sqrt (eps)}.
##
## @strong{Caution:} This is a numerically unstable algorithm and should not
## be used on large polynomials.
##
## Example code:
##
## @example
## @group
## polygcd (poly (1:8), poly (3:12)) - poly (3:8)
## @result{} [ 0, 0, 0, 0, 0, 0, 0 ]
## deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))) - poly (1:2)
## @result{} [ 0, 0, 0 ]
## @end group
## @end example
## @seealso{poly, roots, conv, deconv, residue}
## @end deftypefn

function x = polygcd (b, a, tol)

  if (nargin < 2)
    print_usage ();
  endif

  if (nargin == 2)
    if (isa (a, "single") || isa (b, "single"))
      tol = sqrt (eps ("single"));
    else
      tol = sqrt (eps);
    endif
  endif
  ## FIXME: No input validation of tol if it was user-supplied


  if (length (a) == 1 || length (b) == 1)
    if (a == 0)
      x = b;
    elseif (b == 0)
      x = a;
    else
      x = 1;
    endif
  else
    a /= a(1);
    while (1)
      [d, r] = deconv (b, a);
      nz = find (abs (r) > tol);
      if (isempty (nz))
        x = a;
        break;
      else
        r = r(nz(1):length(r));
      endif
      b = a;
      a = r / r(1);
    endwhile
  endif

endfunction


%!test
%! poly1 = [1 6 11 6]; # (x+1)(x+2)(x+3);
%! poly2 = [1 3 2];    # (x+1)(x+2);
%! poly3 = polygcd (poly1, poly2);
%! assert (poly3, poly2, sqrt (eps));

%!assert (polygcd (poly (1:8), poly (3:12)), poly (3:8), sqrt (eps))
%!assert (deconv (poly (1:8), polygcd (poly (1:8), poly (3:12))), poly (1:2), sqrt (eps))

%!test
%! for ii=1:100
%!   ## Exhibits numerical problems for multipliers of ~4 and greater.
%!   p  = (unique (randn (10, 1)) * 3).';
%!   p1 = p(3:end);
%!   p2 = p(1:end-2);
%!   assert (polygcd (poly (-p1), poly (-p2)),
%!           poly (- intersect (p1, p2)), sqrt (eps));
%! endfor