function [q, r] = poly_long_div(n, d)
  gd = length(d);
  pv = zeros(1, length(n));
  pv(1:gd) = d;
  if ( length(n) >= gd )
    q = [];
    while ( length(n) >= gd )
      q = [q, n(1)/pv(1)];
      n = n - pv .* (n(1)/pv(1));
      n = shift(n, -1);           %
      tn = n(1:length(n)-1);      % eat the higher power term
      n = tn;                     %
      tp = pv(1:length(pv)-1);
      pv = tp;                    % make pv the same length of n
    endwhile
    r = n;
  else
    q = [0];
    r = n;
  endif
endfunction

[q, r] = poly_long_div([1,-12,0,-42], [1,-3]);
polyout(q, 'x');
polyout(r, 'x');
disp("");
[q, r] = poly_long_div([1,-12,0,-42], [1,1,-3]);
polyout(q, 'x');
polyout(r, 'x');
disp("");
[q, r] = poly_long_div([1,3,2], [1,1]);
polyout(q, 'x');
polyout(r, 'x');
disp("");
[q, r] = poly_long_div([1,3], [1,-12,0,-42]);
polyout(q, 'x');
polyout(r, 'x');