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########################################################################
##
## Copyright (C) 1994-2024 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{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])
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