--- a/scripts/polynomial/polyder.m
+++ b/scripts/polynomial/polyder.m
@@ -19,17 +19,27 @@
 
 ## -*- texinfo -*-
 ## @deftypefn {Function File} {} polyder (@var{c})
+## @deftypefnx {Function File} {[@var{q}] =} polyder (@var{b}, @var{a})
+## @deftypefnx {Function File} {[@var{q}, @var{r}] =} polyder (@var{b}, @var{a})
 ## See polyderiv.
 ## @end deftypefn
 
-## Author: jwe
+## Author: John W. Eaton
+## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
+##    handle b/a and b*a
 
-function q = polyder (p)
+function [q, r] = polyder (p, a)
 
   if (nargin == 1)
     q = polyderiv (p);
+  elseif (nargin==2)
+    if (nargout==2)
+      [q, r] = polyderiv (p,a);
+    else
+      q = polyderiv (p,a);
+    endif
   else
-    usage ("polyder (vector)");
+    usage ("q=polyder(p) or q=polyder(b,a) or [q, r]=polyder(b,a)");
   endif
 
 endfunction

--- a/scripts/polynomial/polyderiv.m
+++ b/scripts/polynomial/polyderiv.m
@@ -19,39 +19,77 @@
 
 ## -*- 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}.
+## 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, polyval, and polyvalm}
+## filter, polygcd, polyval, and polyvalm}
 
 ## Author: Tony Richardson <arichard@stark.cc.oh.us>
 ## Created: June 1994
 ## Adapted-By: jwe
-
-function q = polyderiv (p)
+## Paul Kienzle <pkienzle@kienzle.powernet.co.uk>
+##    handle b/a and b*a
 
-  if (nargin != 1)
-    usage ("polyderiv (vector)");
+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 (! isvector (p))
     error ("polyderiv: argument must be a vector");
   endif
 
-  lp = numel (p);
-  if (lp == 1)
-    q = 0;
-    return;
-  elseif (lp == 0)
-    q = [];
-    return;
-  end
+  if (nargin == 2)
+    if (! isvector (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 numel(p) == 1
+	q = -p * polyderiv(a);
+      elseif numel(a) == 1
+	q = a * polyderiv(p);
+      else
+      	q = conv(polyderiv(p),a) - conv(p,polyderiv(a));
+      	q = polyreduce(q);
+      endif
 
-  ## Force P to be a row vector.
-  p = p(:).';
+      ## remove common factors from numerator and denominator
+      x = polygcd(q,r);
+      if length(x)!=1
+      	q=deconv(q,x);
+      	r=deconv(r,x);
+      endif
 
-  q = p(1:(lp-1)) .* [(lp-1):-1:1];
+      ## move all the gain into the numerator
+      q=q/r(1);
+      r=r/r(1);
+    endif
+  else
+    lp = numel (p);
+    if (lp == 1)
+      q = 0;
+      return;
+    elseif (lp == 0)
+      q = [];
+      return;
+    end
+
+    ## Force P to be a row vector.
+    p = p(:).';
+
+    q = p (1:(lp-1)) .* [(lp-1):-1:1];
+  endif
 
 endfunction

new file mode 100644
--- /dev/null
+++ b/scripts/polynomial/polygcd.m
@@ -0,0 +1,65 @@
+## 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} {[@var{q}]} polygcd (@var{b}, @var{a}, @var{tol})
+##
+## Find 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.
+## Tolerance defaults to 
+## @example 
+## sqrt(eps).
+## @end example
+##  Note that this is an unstable
+## algorithm, so don't try it on large polynomials.
+##
+## Example
+## @example
+##    polygcd(poly(1:8),poly(3:12)) - poly(3:8)
+##    deconv(poly(1:8),polygcd(poly(1:8),poly(3:12))) - poly(1:2)
+## @end example
+## @end deftypefn
+##
+## @seealso{poly, polyinteg, polyderiv, polyreduce, roots, conv, deconv,
+## residue, filter, polyval, and polyvalm}
+
+function x = polygcd(b,a,tol)
+  if (nargin<2 || nargin>3)
+    usage("x=polygcd(b,a [,tol])");
+  endif
+  if (nargin<3), tol=sqrt(eps); endif
+  if (length(a)==1 || length(b)==1)
+    if a==0, x=b;
+    elseif b==0, x=a;
+    else x=1;
+    endif
+    return;
+  endif
+  a = a./a(1);
+  while (1)
+    [d, r] = deconv(b, a);
+    nz = find(abs(r)>tol);
+    if isempty(nz)
+      x = a; 
+      return;
+    else
+      r = r(nz(1):length(r));
+    endif
+    b = a;
+    a = r./r(1);
+  endwhile
+endfunction
\ No newline at end of file