% vres = polyadd(v1,v2)
% Performs polynomial addition, and returns the result. All polynomials
% are expressed as vectors with the following format:
% The first element describes the lowest order of the terms in the
% polynomial, while the rest of the elements give the coefficients
% of the terms starting with the lowest order term.
%
% e.g. v = [3 2 4 1] corresponds to 2*x^3+4*x^4+x^5 
%
% George Ginis, May 2001

function vres = polyadd(v1,v2); 
  
  % polynomial length (must be equal for both v1 and v2)
  len = length(v1);
  if (length(v1) ~= length(v2))
    disp('Vectors in polyadd have unequal length!');
    exit;
  end
  
  d1 = v1(1);  % lowest order of polynomial 1
  d2 = v2(1);  % lowest order of polynomial 2
  
  p1 = v1(2:len);  % coefficients of polynomial 1
  p2 = v2(2:len);  % coefficients of polynomial 2
  
  if (d1 == d2)  % polynomials have the same degree
    
    vres(1) = d1;
    vres(2:len) = p1+p2;
    
  elseif (d1 > d2)  % first polynomial has higher degree
     
    diff = d1-d2; 
    p1new=zeros(1,len-1);
    p1new(1+diff:len-1) = p1(1:len-diff-1);  % perform "shift" of p2
    
    vres(1) = d2;
    vres(2:len) = p1new+p2;
    
  else   % (d1 < d2) second polynomial has higher degree 
    
    diff = d2-d1;
    p2new=zeros(1,len-1);
    p2new(1+diff:len-1) = p2(1:len-diff-1);  % perform "shift" of p1
    
    vres(1) = d1;
    vres(2:len) = p1+p2new;
    
  end