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polyderiv.m

## Copyright (C) 1996, 1997 John W. Eaton
##
## 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, 59 Temple Place - Suite 330, Boston, MA
## 02111-1307, USA.

## -*- texinfo -*-
## @deftypefn {Function File} {} polyderiv (@var{c})
## @deftypefnx {Function File} {[@var{q}] =} polyder (@var{b}, @var{a})
## @deftypefnx {Function File} {[@var{q}, @var{r}] =} polyder (@var{b}, @var{a})
## Return the coefficients of the derivative of the polynomial whose
## coefficients are given by vector @var{c}.  If a pair of polynomials
## is given @var{b} and @var{a}, the derivative of the product is
## returned in @var{q}, or the quotient numerator in @var{q} and the
## quotient denominator in @var{r}.
## @end deftypefn
## @seealso{poly, polyinteg, polyreduce, roots, conv, deconv, residue,
## filter, polygcd, polyval, and polyvalm}

## Author: Tony Richardson <arichard@stark.cc.oh.us>
## Created: June 1994
## Adapted-By: jwe
## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
##    handle b/a and b*a

function [q, r] = polyderiv (p, a)

  if (nargin < 1 || nargin > 3)
    usage ("q=polyderiv(p) or q=polyderiv(b,a) or [q, r]=polyderiv(b,a)");
  endif

  if (! is_vector (p))
    error ("polyderiv: argument must be a vector");
  endif

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

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

      ## move all the gain into the numerator
      q=q/r(1);
      r=r/r(1);
    endif
    return;
  endif

  lp = length (p);
  if (lp == 1)
    q = 0;
    return;
  elseif (lp == 0)
    q = [];
    return;
  end

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

endfunction

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