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## -*- texinfo -*-
## @deftypefn  {} {@var{k} =} polyder (@var{p})
## @deftypefnx {} {@var{k} =} polyder (@var{a}, @var{b})
## @deftypefnx {} {[@var{q}, @var{d}] =} polyder (@var{b}, @var{a})
## Return the coefficients of the derivative of the polynomial whose
## coefficients are given by the vector @var{p}.
##
## If a pair of polynomials is given, return the derivative of the product
## @math{@var{a}*@var{b}}.
##
## If two inputs and two outputs are given, return the derivative of the
## polynomial quotient @math{@var{b}/@var{a}}.  The quotient numerator is
## in @var{q} and the denominator in @var{d}.
## @seealso{polyint, polyval, polyreduce}
## @end deftypefn

function [q, d] = polyder (p, a)

  if (nargin < 1)
    print_usage ();
  endif

  if (! isvector (p))
    error ("polyder: argument must be a vector");
  endif
  if (nargin == 2)
    if (! isvector (a))
      error ("polyder: argument must be a vector");
    endif
    if (nargout == 1)
      ## derivative of p*a returns a single polynomial
      q = polyder (conv (p, a));
    else
      ## derivative of p/a returns numerator and denominator
      d = conv (a, a);
      if (numel (p) == 1)
        q = -p * polyder (a);
      elseif (numel (a) == 1)
        q = a * polyder (p);
      else
        q = conv (polyder (p), a) - conv (p, polyder (a));
        q = polyreduce (q);
      endif

      ## remove common factors from numerator and denominator
      x = polygcd (q, d);
      if (length (x) != 1)
        q = deconv (q, x);
        d = deconv (d, x);
      endif

      ## move all the gain into the numerator
      q /= d(1);
      d /= d(1);
    endif
  else
    lp = numel (p);
    if (lp == 1)
      q = 0;
      return;
    elseif (lp == 0)
      q = [];
      return;
    endif

    ## Force P to be a row vector.
    p = p(:).';

    q = p(1:(lp-1)) .* [(lp-1):-1:1];
  endif

endfunction


%!assert (polyder ([1, 2, 3], [2, 2]))
%!assert (polyder (13), 0)

%!error polyder ([])
%!error polyder (1,2,3)
%!error <argument must be a vector> polyder ([1, 2; 3, 4])