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## -*- texinfo -*-
## @deftypefn  {} {@var{q} =} polyint (@var{p})
## @deftypefnx {} {@var{q} =} polyint (@var{p}, @var{k})
## Return the coefficients of the integral of the polynomial whose
## coefficients are represented by the vector @var{p}.
##
## The variable @var{k} is the constant of integration, which by default is
## set to zero.
## @seealso{polyder, polyval}
## @end deftypefn

function q = polyint (p, k)

  if (nargin < 1)
    print_usage ();
  endif

  if (nargin == 1)
    k = 0;
  elseif (! isscalar (k))
    error ("polyint: the constant of integration must be a scalar");
  endif

  if (! (isvector (p) || isempty (p)))
    error ("polyint: argument must be a vector");
  endif

  lp = length (p);

  if (lp == 0)
    q = [];
    return;
  endif

  if (rows (p) > 1)
    ## Convert to column vector
    p = p.';
  endif

  q = [(p ./ [lp:-1:1]), k];

endfunction


%!test
%! A = [3, 2, 1];
%! assert (polyint (A), polyint (A,0));
%! assert (polyint (A), polyint (A'));
%! assert (polyint (A), [1, 1, 1, 0]);
%! assert (polyint (A,1), ones (1,4));

%!test
%! A = ones (1,8);
%! B = [length(A):-1:1];
%! assert (polyint (A), [1./B, 0]);

%!error <Invalid call> polyint ()
%!error polyint (ones (2,2))